The cosines of the angle between any two diagonals of a cube is:
- ✓$\frac{1}{3}$
- B$\frac{1}{2}$
- C$\frac{2}{3}$
- D$\frac{1}{\sqrt{3}}$
Answer: A.
View full solution →Question types
Three Dimensional Geometry question types
300 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
300
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
229 Q→02Assertion (A) & Reason (B) MCQ
10 Q→032 Marks Questions
15 Q→043 Marks Question
17 Q→055 Marks Questions
5 Q→06Case study (4 Marks)
10 Q→07Fill In The Blanks[1 Marks ]
6 Q→08True False[1 Marks ]
8 Q→Sample Questions
Three Dimensional Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The $xy-$plane divided the line joining the point $(-1, 3, 4)$ and $(2, -5, 6)$
- AInternally in the ratio $2 : 3$
- ✓Externally in the ratio $2 : 3$
- CInternally in the ratio $3 : 2$
- DExternally in the ratio $3 : 2$
Answer: B.
View full solution →A line $OP$ where $O = (0, 0, 0)$ makes equal angles with $ox, oy, oz.$ The point on $OP,$ which is at a distance of $6$ units from $O$ is:
- ✓$\Big(\frac{6}{\sqrt{3}},\frac{6}{\sqrt{3}},\frac{6}{\sqrt{3}}\Big)$
- B$\big(2\sqrt{3},-2\sqrt{3},2\sqrt{3}\big)$
- C$-\big(2\sqrt{3},-2\sqrt{3},2\sqrt{3}\big)$
- D$-\big(6\sqrt{3},-6\sqrt{3},6\sqrt{3}\big)$
Answer: A.
View full solution →Choose the correct answer from the given four options. The locus represented by $xy + yz = 0$ is:
- AA pair of perpendicular lines.
- BA pair of parallel lines.
- CA pair of parallel planes.
- ✓A pair of perpendicular planes.
Answer: D.
View full solution →The equation $x^2- x - 2 = 0$ in three dimensional space is represented by:
- ✓A pair of parallel planes
- BA pair of straight lines
- CA pair of perpendicular plane
- DNone of these
Answer: A.
View full solution →Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given. Choose the correct answer out of the following choices:
Assertion: If the cartesian equation of a line is $\frac{\text{x}-5}{3}=\frac{\text{y}+4}{7}=\frac{\text{z}-6}{2},$ then its vector form is $\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda(3\hat{\text{i}}+7\hat{\text{j}}+2\hat{\text{k}}).$
Reason: The cartesian equation of the line which passes through the point $(-2, 4, -5)$ and parallel to the line given by $\frac{\text{x}+3}{3}=\frac{\text{y}-4}{5}=\frac{\text{z}+8}{6}$ is $\frac{\text{x}+3}{-2}=\frac{\text{y}-4}{4}=\frac{\text{z}+8}{-5}.$
Assertion: If the cartesian equation of a line is $\frac{\text{x}-5}{3}=\frac{\text{y}+4}{7}=\frac{\text{z}-6}{2},$ then its vector form is $\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda(3\hat{\text{i}}+7\hat{\text{j}}+2\hat{\text{k}}).$
Reason: The cartesian equation of the line which passes through the point $(-2, 4, -5)$ and parallel to the line given by $\frac{\text{x}+3}{3}=\frac{\text{y}-4}{5}=\frac{\text{z}+8}{6}$ is $\frac{\text{x}+3}{-2}=\frac{\text{y}-4}{4}=\frac{\text{z}+8}{-5}.$
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓Assertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Points $A(4, 0, 4), B(1, 2, 3), C(-2, 4, 2)$ are collinear.
Reason: Three points $A, B, C$ are collinear if $AB + BC = AC$ and $AB, BC < AC.$
Assertion: Points $A(4, 0, 4), B(1, 2, 3), C(-2, 4, 2)$ are collinear.
Reason: Three points $A, B, C$ are collinear if $AB + BC = AC$ and $AB, BC < AC.$
- ✓Both Assertion $\&$ Reason are individually true $\&$ Reason is correct explanation of Assertion.
- BBoth Assertion $\&$ Reason are individually true but Reason is not the, correct $($proper$)$ explanation of Assertion.
- CAssertion is true but Reason is false.
- DAssertion is false but Reason is true.
Answer: A.
View full solution →Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : The points $(1, 2, 3), (-2, 3, 4)$ and $(7, 0, 1)$ are collinear
Reason : If a line makes angles $\frac{\pi}{2}, \frac{3\pi}{4}$ and $\frac{\pi}{4}$ with $X, Y,$ and $Z -$ axes respectively, then its direction cosines are $0,\frac{-1}{\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$
Assertion : The points $(1, 2, 3), (-2, 3, 4)$ and $(7, 0, 1)$ are collinear
Reason : If a line makes angles $\frac{\pi}{2}, \frac{3\pi}{4}$ and $\frac{\pi}{4}$ with $X, Y,$ and $Z -$ axes respectively, then its direction cosines are $0,\frac{-1}{\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- ✓Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: B.
View full solution →Assertion $(A):$ The lines $\vec{r}=\vec{a}_1+\lambda \vec{b}_1$ and $\vec{r}=\vec{a}_2+\mu \vec{b}_2$ are perpendicular, when $\vec{b}_1 \cdot \vec{b}_2=0$.
Reason $(R):$ The angle $\theta$ between the lines $\vec{r}=\vec{a}_1+\lambda \vec{b}_1$ and $\vec{r}=\vec{a}_2+\mu \vec{b}_2$ is given by $\cos \theta=\frac{\vec{b}_1 \cdot \vec{b}_2}{\left|\vec{b}_1\right|\left|\vec{b}_2\right|}$.
Reason $(R):$ The angle $\theta$ between the lines $\vec{r}=\vec{a}_1+\lambda \vec{b}_1$ and $\vec{r}=\vec{a}_2+\mu \vec{b}_2$ is given by $\cos \theta=\frac{\vec{b}_1 \cdot \vec{b}_2}{\left|\vec{b}_1\right|\left|\vec{b}_2\right|}$.
- ABoth Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is the correct explanation of Assertion $(A).$
- ✓Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is not the correct explanation of Assertion $(A).$
- CAssertion $(A)$ is true but Reason $(R)$ is false.
- DAssertion $(A)$ is false but Reason $(R)$ is true.
Answer: B.
View full solution →Assertion (A) : Quadrilateral formed by vertices $A(0,0,0), B(3,4,5), C(8,8,8)$ and $D(5,4,3)$ is a rhombus. Reason $(R): A B C D$ is a rhombus if $A B=B C=C D=D A$, $A C \neq B D$.
- ✓Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is the correct explanation of the Assertion $(A).$
- BBoth Assertion $(A)$ and Reason $(R)$ are true, but Reason $(R)$ is not the correct explanation of the Assertion $(A).$
- CAssertion $(A)$ is true, but Reason $(R)$ is false.
- DAssertion $(A)$ is false, but Reason $(R)$ is true.
Answer: A.
View full solution →If the lines $\frac{{x - 1}}{{ - 3}} = \frac{{y - 2}}{{2k}} = \frac{{z - 3}}{2}$ and $\frac{{x - 1}}{{3k}} = \frac{{y - 1}}{1} = \frac{{z - 6}}{{ - 5}}$ are perpendicular, find the value of 'k'.
View full solution →Find the equation of a line parallel to x-axis and passing through the origin.
The Cartesian equation of a line is $\frac{{x - 5}}{3} = \frac{{y + 4}}{7} = \frac{{z - 6}}{2}$. Write its vector form.
View full solution →Find the cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by$\frac{{x + 3}}{3} = \frac{{y - 4}}{5} = \frac{{z + 8}}{6}$.
View full solution →Find the equation of the line in cartesian form that passes through the point with position vector $2\hat i - \hat j + 4\hat k$ and is in the direction $\hat i + 2\hat j - \hat k$.
View full solution →Find the vector equation of the line passing through the point (1, 2, -4) and perpendicular to the two lines:$ \frac { x - 8 } { 3 } = \frac { y + 19 } { - 16 } = \frac { z - 10 } { 7 }$ and $ \frac { x - 15 } { 3 } = \frac { y - 29 } { 8 } = \frac { z - 5 } { - 5 }.$
View full solution →Find the shortest distance between lines $\vec{r}=6 \hat{i}+2 \hat{j}+2 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k})$ and $\vec{r}=-4 \hat{i}-\hat{k}+\mu(3 \hat{i}-2 \hat{j}-2 \hat{k})$
View full solution →Find the angle between the lines whose direction ratios are a, b, c and b - c, c - a, a - b.
Find the angle between the lines $\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$ and $\frac{{x - 5}}{4} = \frac{{y - 2}}{1} = \frac{{z - 3}}{8}$.
View full solution →Find the angle between the lines $\frac{{x - 2}}{2} = \frac{{y - 1}}{5} = \frac{{z + 3}}{{ - 3}}$ and $\frac{{x + 2}}{{ - 1}} = \frac{{y - 4}}{8} = \frac{{z - 5}}{4}$.
View full solution →Find the shortest distance between the lines whose vector equations are $ \vec r = \left( {1 - t} \right)\hat i + (t - 2)\hat j + (3 - 2t)\hat k$ and $\vec r = \left( {s + 1} \right)\hat i + (2s - 1)\hat j - (2s + 1)\hat k$
View full solution →Find the shortest distance between the lines $\frac{{x + 1}}{7} = \frac{{y + 1}}{{ - 6}} = \frac{{z + 1}}{1}$ and $\frac{{x - 3}}{1} = \frac{{y - 5}}{{ - 2}} = \frac{{z - 7}}{1}$
View full solution →Find the direction cosines of the sides of the triangle whose vertices are $(3, 5, -4), (-1, 1, 2)$ and $(-5, -5, -2).$
View full solution →Find the vector and Cartesian equations of the line through the point (5, 2, -4) and which is parallel to the vector $3\hat i + 2\hat j - 8\hat k$.
View full solution →Find the distance between the lines $l_1$ and $l_2$ given by
$\vec r = \hat i + 2\hat j - 4\hat k + \lambda (2\hat i + 3\hat j + 6\hat k)$
and $\vec r = 3\hat i + 3\hat j - 5\hat k + \mu (2\hat i + 3\hat j + 6\hat k)$
View full solution →$\vec r = \hat i + 2\hat j - 4\hat k + \lambda (2\hat i + 3\hat j + 6\hat k)$
and $\vec r = 3\hat i + 3\hat j - 5\hat k + \mu (2\hat i + 3\hat j + 6\hat k)$
Suppose the floor of a hotel is made up of mirror polished Kota stone. Also, there is a large crystal chandelier attached at the ceiling of the hotel. Consider the floor of the hotel as a plane having equation $x - 2y + 2z = 3$ and crystal chandelier at the point $(3, -2, 1)$.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The d.r'.s of the perpendicular from the point $(3, -2, 1)$ to the plane $x - 2y + 2z = 3,$ is:
- $< 1, 2, 2 >$
- $< 1, -2, 2 >$
- $< 2, 1, 2 >$
- $< 2, -1, 2 >$
- The length of the perpendicular from the point $(3, -2, 1)$ to the plane $x - 2y + 2z = 3,$ is:
- $\frac{2}{3}\text{units}$
- $3$ units
- $2$ units
- None of these
- The equation of the perpendicular from the point $(3, -2, 1)$ to the plane $x - 2y + 2z = 3$, is:
- $\frac{\text{x}-3}{1}=\frac{\text{y}-2}{-2}=\frac{\text{z}-1}{2}$
- $\frac{\text{x}-3}{1}=\frac{\text{y}+2}{-2}=\frac{\text{z}-1}{2}$
- $\frac{\text{x}+3}{1}=\frac{\text{y}+2}{-2}=\frac{\text{z}-1}{2}$
- None of these
- The equation of plane parallel to the plane $x - 2y + 2z = 3,$ which is at a unit distance from the point $(3, -2, 1)$ is:
- $x - 2y + 2z = 0$
- $x - 2y + 2z = 6$
- $x - 2y + 2z = 12$
- Both $(b)$ and $(c)$
- The image of the point $(3, -2, 1)$ in the given plane is:
- $\Big(\frac{5}{3},\frac{2}{3},\frac{-5}{3}\Big)$
- $\Big(\frac{-5}{3},\frac{-2}{3},\frac{5}{3}\Big)$
- $\Big(\frac{-5}{3},\frac{2}{3},\frac{5}{3}\Big)$
- None of these
Consider the following diagram, where the forces in the cable are given. 
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions.
- The equation of line along the cable AD is:
- $\frac{\text{x}}{5}=\frac{\text{y}}{4}=\frac{\text{z}-30}{15}$
- $\frac{\text{x}}{4}=\frac{\text{y}}{5}=\frac{\text{z}-30}{15}$
- $\frac{\text{x}}{5}=\frac{\text{y}}{4}=\frac{30-\text{z}}{15}$
- $\frac{\text{x}}{4}=\frac{\text{y}}{5}=\frac{30-\text{z}}{15}$
- The length of cable DC is:
- $4\sqrt{61}\text{m}$
- $5\sqrt{61}\text{m}$
- $6\sqrt{61}\text{m}$
- $7\sqrt{61}\text{m}$
- The vector DB is:
- $-6\hat{\text{i}}+4\hat{\text{j}}-30\hat{\text{k}}$
- $6\hat{\text{i}}-4\hat{\text{j}}+30\hat{\text{k}}$
- $6\hat{\text{i}}+4\hat{\text{j}}+30\hat{\text{k}}$
- None of these
- The sum of vectors along the cables is:
- $17\hat{\text{i}}+6\hat{\text{j}}+90\hat{\text{k}}$
- $17\hat{\text{i}}-6\hat{\text{j}}-90\hat{\text{k}}$
- $17\hat{\text{i}}+6\hat{\text{j}}-90\hat{\text{k}}$
- None of these
- The sum of distances of points A, B and C from the origin, i.e., OA + OB + OC is:
- $\sqrt{164}+\sqrt{52}+\sqrt{625}$
- $\sqrt{52}+\sqrt{625}+\sqrt{48}$
- $\sqrt{164}+\sqrt{625}+\sqrt{49}$
- None of these
Consider the following diagram, where the forces in the cable are given. 
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions.
- The cartesian equation of line along EA is:
- $\frac{\text{x}}{-4}=\frac{\text{y}}{3}=\frac{\text{z}}{12}$
- $\frac{\text{x}}{-4}=\frac{\text{y}}{3}=\frac{\text{z}-24}{12}$
- $\frac{\text{x}}{-3}=\frac{\text{y}}{3}=\frac{\text{z}-12}{12}$
- $\frac{\text{x}}{3}=\frac{\text{y}}{4}=\frac{\text{z}-24}{12}$
- The vector $\overline{\text{ED}}$ is:
- $8\hat{\text{i}}-6\hat{\text{j}}+24\hat{\text{k}}$
- $-8\hat{\text{i}}-6\hat{\text{j}}+24\hat{\text{k}}$
- $-8\hat{\text{i}}-6\hat{\text{j}}-24\hat{\text{k}}$
- $8\hat{\text{i}}+6\hat{\text{j}}+24\hat{\text{k}}$
- The length of the cable EB is:
- 24 units
- 26 units
- 27 units
- 25 units
- The length of cable EC is equal to the length of:
- EA
- EB
- ED
- All of these
- The sum of all vectors along the cables is:
- $96\hat{\text{i}}$
- $96\hat{\text{j}}$
- $-96\hat{\text{k}}$
- $96\hat{\text{k}}$
If $a_{1,} b_{1,} c_{1,}$ and $a_{2,}b_{2,} c_2$ are direction ratios of two lines say $L_1$ and $L_2$ respectively. Then $L_1 || L_2$ iff $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$ and $\text{L}_1\perp\text{L}_2$ iff $a_1a_2 + b_1b_2 + c_1c_2 = 0.$
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- If $l_{1,} m_1, n_{1,}$ and $l_2, m_2, n_2$ are the direction cosines of $L_1$ and $L_2$ respectively, then $L_1$ will be perpendicular to $L_2$, iff:
- $l_1l_2 + m_1m_2 + n_1n_2 = 0$
- $l_1m_2 + m_1l_2 + n_1n_2 = 0$
- $\frac{\text{l}_1}{\text{l}_2}=\frac{\text{m}_1}{\text{m}_2}=\frac{\text{n}_1}{\text{n}_2}$
- None of these
- If $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are direction cosines of $L_1$ and $L_2$ respectively, then $L_1$ will be parallel to $L_2,$ iff:
- $l_1l_2 + m_1m_2 + n_1n_2 = 0$
- $l_1m_2 + m_1l_2 + n_1n_2 = 0$
- $\frac{\text{l}_1}{\text{l}_2}=\frac{\text{m}_1}{\text{m}_2}=\frac{\text{n}_1}{\text{n}_2}$
- $m_1n_2 + m_2n_2 + l_1l_2 = 0$
- The coordinates of the foot of the perpendicular drawn from the point $A(1, 2, 1)$ to the line joining $B(1, 4, 6)$ and $C(5, 4, 4),$ are:
- $(1, 2, 1)$
- $(2, 4, 5)$
- $(3, 4, 5)$
- $(3, 4, 5)$
- The direction ratios of the line which is perpendicular to the lines with direction ratios proportional to $(1, -2, -2)$ and $(0, 2, 1)$ are:
- $< 1, 2, 1 >$
- $< 2,-1, 2 >$
- $< -1,2, 2 >$
- None of these
- The lines $\frac{\text{x}-2}{3}=\frac{\text{y}+1}{-2}=\frac{\text{z}-2}{0}$ and $\frac{\text{x}-1}{1}=\frac{\frac{\text{y}+3}{2}}{\frac{3}{2}}=\frac{\text{z}+5}{2}$ are:
- Parallel.
- Perpendicular.
- Skew lines.
- Non-intersecting.
Two motorcycles A and Bare running at the speed more than allowed speed on the road along the lines $\vec{\text{r}}=\lambda(\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}})$ and $\vec{\text{r}}=3\hat{\text{i}}+3\hat{\text{j}}+\mu(2\hat{\text{i}+\hat{\text{j}}+\hat{\text{k}}}),$ respectively. 
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions.
- The cartesian equation of the line along which motorcycle A is running is:
- $\frac{\text{x}+1}{1}=\frac{\text{y}+1}{2}=\frac{\text{z}-1}{-1}$
- $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{-1}$
- $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{1}$
- None of these
- The direction cosines of line along which motorcycle A is running, are:
- < 1, -2, 1 >
- < I, 2, -1 >
- $<\frac{1}{\sqrt{6}},\frac{-2}{\sqrt{6}},\frac{1}{\sqrt{6}}>$
- $<\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}},\frac{-1}{\sqrt{6}}>$
- The direction ratios of line along which motorcycle Bis running, are:
- < 1, 0, 2 >
- < 2, 1, 0 >
- < 1, 1, 2 >
- < 2, 1, 1 >
- The shortest distance between the gives lines is:
- 4 units
- $2\sqrt{3}\text{ units}$
- $3\sqrt{2}\text{ units}$
- 0 units
- The motorcycles will meet with an accident at the point:
- (-1, 1, 2)
- (2, 1, -1)
- (1, 2, -1)
- Does not exist
Fill in the blanks.
The vector equation of the line through the points (3, 4, -7) and (1, -1, 6) is __________.
The vector equation of the line through the points (3, 4, -7) and (1, -1, 6) is __________.
Fill in the blanks.
The cartesian equation of the plane $\vec{\text{r}}\cdot(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}})=2$ is ________.
View full solution →The cartesian equation of the plane $\vec{\text{r}}\cdot(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}})=2$ is ________.
Fill in the blanks.
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is __________.
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is __________.
The position vectors of two points A and B are $\overrightarrow{\text{OA}}=2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}}$ and $\overrightarrow{\text{OB}}=2\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}},$ respectively. The position vector of a point P which divides the line segment joining A and B in the ratio 2 : 1 is ___________.
View full solution →Fill in the blanks.
The vector equation of the line $\frac{\text{x}-5}{3}=\frac{\text{y}+4}{7}=\frac{\text{z}-6}{2}$ is _________.
View full solution →The vector equation of the line $\frac{\text{x}-5}{3}=\frac{\text{y}+4}{7}=\frac{\text{z}-6}{2}$ is _________.
State True or False for the following:
The line $\vec{\text{r}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}+\lambda({\text{i}}-{\text{j}}+2{\text{k}})$ lies in the plane $\vec{\text{r}}\cdot(3\hat{\text{i}}+{\text{j}}-{\text{k}})+2=0$
View full solution →The line $\vec{\text{r}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}+\lambda({\text{i}}-{\text{j}}+2{\text{k}})$ lies in the plane $\vec{\text{r}}\cdot(3\hat{\text{i}}+{\text{j}}-{\text{k}})+2=0$
State True or False for the following: The angle between the line $\vec{\text{r}}=(5\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}})+\lambda(2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}})$ and the plane $\vec{\text{r}}(3\hat{\text{i}}-4\hat{\text{j}}-\hat{\text{k}})+5=0$ is $\sin^{-1}\Big(\frac{5}{2\sqrt{91}}\Big).$
View full solution →State True or False for the following:
The equation of a line, which is parallel to $2\hat{\text{i}}+\hat{\text{j}}+3\hat{\text{k}}$ and which passes through the point (5, -2, 4) is $\frac{\text{x}-5}{2}=\frac{\text{y}-5}{-1}=\frac{\text{z}-4}{3}.$
View full solution →The equation of a line, which is parallel to $2\hat{\text{i}}+\hat{\text{j}}+3\hat{\text{k}}$ and which passes through the point (5, -2, 4) is $\frac{\text{x}-5}{2}=\frac{\text{y}-5}{-1}=\frac{\text{z}-4}{3}.$
State True or False for the following:
The intercepts made by the plane 2x - 3y + 5z + 4 = 0 on the co-ordinate axis are $-2, \frac{4}{3},-\frac{4}{5}.$
View full solution →The intercepts made by the plane 2x - 3y + 5z + 4 = 0 on the co-ordinate axis are $-2, \frac{4}{3},-\frac{4}{5}.$
State True or False for the following:
The vector equation of the line $\frac{\text{x}-5}{3}=\frac{\text{y}-4}{7}=\frac{\text{z}-6}{2}$ is $\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda(3\hat{\text{i}}-7\hat{\text{j}}+2\hat{\text{k}}).$
View full solution →The vector equation of the line $\frac{\text{x}-5}{3}=\frac{\text{y}-4}{7}=\frac{\text{z}-6}{2}$ is $\vec{\text{r}}=5\hat{\text{i}}-4\hat{\text{j}}+6\hat{\text{k}}+\lambda(3\hat{\text{i}}-7\hat{\text{j}}+2\hat{\text{k}}).$
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