Sample QuestionsDirection Cosines and Direction Ratios 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 $(2, -5, 6)$
- A
Internally in the ratio $2 : 3$
- ✓
Externally in the ratio $2 : 3$
- C
Internally in the ratio $3 : 2$
- D
Externally in the ratio $3 : 2$
Answer: B.
View full solution →For every point $P(x, y, z)$ on the $x-$axis $($except the origin$),$
- A
$x = 0, y = 0, z ≠ 0$
- B
$y = 0, z = 0, y ≠$ 0
- ✓
$y = 0, z = 0, x ≠ 0$
- D
$x = y = z = 0$
Answer: C.
View full solution →If $O$ is the origin, $OP = 3$ with direction ratios proportional to $-1, 2, -2$ then the coordinates of $P$ are:
Answer: A.
View full solution →$A(3, 2, 0), B(5, 3, 2)$ and $C(-9, 6, -3)$ are the vertices of a tringle $\text{ABC.}$ if the bisector of $\angle\text{ABC}$ meets $BC$ at $D,$ then coordinates of $D$ are:
- ✓
$\Big(\frac{19}{8},\frac{57}{16},\frac{17}{16}\Big)$
- B
$\Big(-\frac{19}{8},\frac{57}{16},\frac{17}{16}\Big)$
- C
$\Big(\frac{19}{8},-\frac{57}{16},\frac{17}{16}\Big)$
- D
$\text{none of these}$
Answer: A.
View full solution →Ratio in which the $xy-$plane divided the join of $(1, 2, 3)$ and $(4, 2, 1)$ is:
- A
$3 : 1$ internally
- ✓
$3 : 1$ externally
- C
$2 : 1$ internally
- D
$2 : 1$ externally
Answer: B.
View full solution →What are the direction cosines of Z-axis?
If a line has direction ratios proportional to 2, -1, -2, then what are its direction consines?
Write the distance of the point P(x, y, z) from XOY plane.
Write the inclination a line with z-axis, if its direction ratios are proportional to 0, 1, -1.
Write the distance of the point (3, −5, 12) from X-axis?
Find the direction cosines of the line passing through two points $(-2, 4, -5)$ and $(1, 2, 3).$
View full solution →Show that the line joining the origin to the point $(2, 1, 1)$ is perpendicular to the line determined by the points $(3, 5, -1)$ and $(4, 3, -1).$
View full solution →Show that the line through points $(4,7,8)$ and $(2,3,4)$ is parallel to the line throught the points $(-1,-2,1)$ and $(1,2,5)$.
View full solution →A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.
If a unit vector $\vec{\text{a}}$ makes an angle $\frac{\pi}{3}$ with $\hat{\text{i}},\frac{\pi}{4}$ with $\hat{\text{j}}$ and an acute angle $\theta$ with $\hat{\text{k}}$, and ,then find the value of $\theta$.
View full solution →Find the angle between the lines whose direction cosines are given by the equations:
$l + m +n = 0$ and $l^2 + m^2 + n^2 = 0$
View full solution →If the coordinates of the points $A, B, C$, are $(1,2,3),(4,5,6),(-4,3,-6)$ and $(2,9,2)$, then find the angle between $A B$ and $C D$.
View full solution →Find the direction cosines of the lines, connected by the relations: $l + m + n = 0$ and $\frac{2}{\text{m}}+\frac{2}{\text{n}}-\text{mn}=0$.
View full solution →Find the angle between the lines whose direction ratios are proportional to a, b, c and b - c, c - a, a - b.
Show that the points $(2, 3, 4), (-1, -2, 1), (5, 8, 7)$ are collinear.
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