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Straight line in space MATHS - Straight line in space

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - English Medium). 136 questions in this chapter.

Question types

Straight line in space question types

136 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

136
Questions
4
Question groups
5
Question types
Sample Questions

Straight line in space questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The direction ratios of the line x - y + z - 5 = 0 = x - 3y - 6 are proportional to:
  1. $3,1,-2$
  2. $2,-4,1$
  3. $\frac{3}{\sqrt{14}},\frac{1}{\sqrt{14}},\frac{-2}{\sqrt{14}}$
  4. $\frac{2}{\sqrt{41}},\frac{-4}{\sqrt{41}},\frac{1}{\sqrt{41}}$
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Q 2M.C.Q (1 Marks)1 Mark
If a line makes angle $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with x-axis and y-axis respectively, then the angle made by the line with z-axis is:
  1. $\frac{\pi}{2}$
  2. $\frac{\pi}{3}$
  3. $\frac{\pi}{4}$
  4. $\frac{5\pi}{12}$
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Q 3M.C.Q (1 Marks)1 Mark
The shortest distance between the lines $\frac{\text{x}-3}{3}=\frac{\text{y}-8}{-1}=\frac{\text{z}-3}{1}$ and, $\frac{\text{x}+3}{-3}=\frac{\text{y}+7}{2}=\frac{\text{z}-6}{4}$ is:
  1. $\sqrt{30}$
  2. $2\sqrt{30}$
  3. $5\sqrt{30}$
  4. $3\sqrt{30}$
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Q 4M.C.Q (1 Marks)1 Mark
The direction ratios of the line perprndicular to the lines $\frac{\text{x}-7}{2}=\frac{\text{y}+17}{-3}=\frac{\text{z}-6}{1}$ and, $\frac{\text{x}+5}{1}=\frac{\text{y}+3}{2}=\frac{\text{z}-4}{-2}$ are proportional to:
  1. 4, 5, 7
  2. 4, -5, 7
  3. 4, -5, -7
  4. -4, 5, 7
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Q 5M.C.Q (1 Marks)1 Mark
The projections of a line segment on x, y and z axes are 12, 4 and 3 respectively. The length and direction cosines of the line segment are:
  1. $13;\frac{12}{13},\frac{4}{13},\frac{3}{13}$
  2. $19;\frac{12}{19},\frac{4}{19},\frac{3}{19}$
  3. $11;\frac{12}{11},\frac{14}{11},\frac{3}{11}$
  4. $\text{None of these}$
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Q 72 Marks Questions2 Marks
Write the formula for the shortest distance between the lines$\vec{\text{r}}=\vec{\text{a}}_1+\lambda\vec{\text{b}}$ and $\vec{\text{r}}=\vec{\text{a}}_2+\mu\vec{\text{b}}.$
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Q 82 Marks Questions2 Marks
The equations of a line are given by $\frac{4-\text{x}}{3}=\frac{\text{y}+3}{3}=\frac{\text{z}+2}{6}.$ Write the direction cosines of a line parallel to this line.
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Q 92 Marks Questions2 Marks
Find the Cartesian equations of the line which passes through the point (-2, 4, -5) and is parallel to the line $\frac{\text{x}+3}{3}=\frac{4-\text{y}}{5}=\frac{\text{z}+8}{6}.$
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Q 123 Marks Question3 Marks
Cartesian equations of a line AB are $\frac{2\text{x}-1}{2}=\frac{4-\text{y}}{7}=\frac{\text{z}+1}{2}.$ Write the direction ratios of a parallel to AB.
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Q 133 Marks Question3 Marks
A line passes throuth the point with position vector $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and is in the direction of $3\hat{\text{i}}+4\hat{\text{j}}-5\hat{\text{k}}.$ Find equations of the line in vector and cartesian form.
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Q 153 Marks Question3 Marks
It the lines $\frac{\text{x}-1}{-3}=\frac{\text{y}-2}{2\lambda}=\frac{\text{z}-3}{2}$ and $\frac{\text{x}-1}{3\lambda}=\frac{\text{y}-2}{1}=\frac{\text{z}-6}{-5}$ are perpendicular, find the value of $\lambda.$
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Q 165 Marks Questions5 Marks
Show that the lines $\frac{\text{x}-1}{3}=\frac{\text{y}+1}{2}=\frac{\text{z}-1}{5}$ and $\frac{\text{x}+2}{4}=\frac{\text{y}-1}{3}=\frac{\text{z}+1}{-2}$ do not intersect.
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Q 175 Marks Questions5 Marks
Find the angle between the following pairs of lines:$\frac{\text{x}-5}{1}=\frac{2\text{y}+6}{-2}=\frac{\text{z}-3}{1}$ and $\frac{\text{x}-2}{3}=\frac{\text{y}+1}{4}=\frac{\text{z}-6}{5}$
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Q 185 Marks Questions5 Marks
Find the angle between the following pairs of lines:$\frac{5-\text{x}}{-2}=\frac{\text{y}+3}{1}=\frac{1-\text{z}}{3}$ and $\frac{\text{x}}{3}=\frac{1-\text{y}}{-2}=\frac{\text{z}+5}{-1}$
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Q 195 Marks Questions5 Marks
Find the equation of the line passing through the points $(1, -1, 1)$ and perpendicular to the lines joining the points $(4, 3, 2), (1, -1, 0)$ and $(1, 2, -1) (2, 1, 1).$
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Q 205 Marks Questions5 Marks
Find the equation of line passing through the point $A(0, 6, -9)$ and $B(-3, -6, 3).$ If $D$ is the foot of perpendicular drawn from a point $C(7, 4, -1)$ on the line $AB,$ then find the coordiantes of the point $D$ and the equation of line $CD.$
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