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Straight line in space Maths - Straight line in space

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 135 questions in this chapter.

Question types

Straight line in space question types

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

135
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 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:
  • ✓
    $13;\frac{12}{13},\frac{4}{13},\frac{3}{13}$
  • B
    $19;\frac{12}{19},\frac{4}{19},\frac{3}{19}$
  • C
    $11;\frac{12}{11},\frac{14}{11},\frac{3}{11}$
  • D
    $\text{None of these}$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
The angle between the straight lines $\frac{\text{x}+1}{2}=\frac{\text{y}-2}{5}=\frac{\text{z}+3}{4}$ and $\frac{\text{x}-1}{1}=\frac{\text{y}+2}{2}=\frac{\text{z}-3}{-3}$ is:
  • A
    45°
  • B
    30°
  • C
    60°
  • ✓
    90°

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
The direction ratios of the line x - y + z - 5 = 0 = x - 3y - 6 are proportional to:
  • ✓
    $3,1,-2$
  • B
    $2,-4,1$
  • C
    $\frac{3}{\sqrt{14}},\frac{1}{\sqrt{14}},\frac{-2}{\sqrt{14}}$
  • D
    $\frac{2}{\sqrt{41}},\frac{-4}{\sqrt{41}},\frac{1}{\sqrt{41}}$

Answer: A.

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Q 4M.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:
  • A
    $\frac{\pi}{2}$
  • ✓
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{4}$
  • D
    $\frac{5\pi}{12}$

Answer: B.

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Q 5M.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:
  • A
    $\sqrt{30}$
  • B
    $2\sqrt{30}$
  • C
    $5\sqrt{30}$
  • ✓
    $3\sqrt{30}$

Answer: D.

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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 102 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 113 Marks Question3 Marks
If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines AB and CD.
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Q 143 Marks Question3 Marks
Find the equation of the line passing through the points (2, 1, 3) and perpendicular to the lines $\frac{\text{x}-1}{1}=\frac{\text{y}-2}{2}=\frac{\text{z}-3}{3}$ and $\frac{\text{x}}{-3}=\frac{\text{y}}{2}=\frac{\text{z}}{5}$
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Q 153 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 165 Marks Questions5 Marks
Find the shortest distance between the following pairs of lines whose cartesian equation are:
$\frac{\text{x}-1}{2}=\frac{\text{y}-2}{3}=\frac{\text{z}-3}{4}$ and $\frac{\text{x}-2}{3}=\frac{\text{y}-3}{4}=\frac{\text{z}-5}{5}$
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Q 175 Marks Questions5 Marks
By computing the shortest distance determine whether the following pairs of lines intersect or not:
$\vec{\text{r}}=\big(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}\big)+\lambda\big(3\hat{\text{i}}-\hat{\text{j}}\big)$ and $\vec{\text{r}}=\big(4\hat{\text{i}}-\hat{\text{k}}\big)+\mu\big(2\hat{\text{i}}+3\hat{\text{k}}\big)$
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Q 185 Marks Questions5 Marks
Find the shortest distance between the following pairs of lines whose vector equation are:
$\vec{\text{r}}=\big(\hat{\text{i}}+\hat{\text{j}}\big)+\lambda\big(2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big)$ and $\vec{\text{r}}=2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}+\mu\big(3\hat{\text{i}}-5\hat{\text{j}}+2\hat{\text{k}}\big)$
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Q 195 Marks Questions5 Marks
Find the shortest distance between the following pairs of lines whose vector equation are:
$\vec{\text{r}}=(\lambda-1)\hat{\text{i}}+(\lambda+1)\hat{\text{j}}-(1+\lambda)\hat{\text{k}}$ and $\vec{\text{r}}=(1-\mu)\hat{\text{i}}+(2\mu-1)\hat{\text{j}}+(\mu+2)\hat{\text{k}}$
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Q 205 Marks Questions5 Marks
By computing the shortest distance determine whether the following pairs of lines intersect or not:3
$\frac{\text{x}-5}{4}=\frac{\text{y}-7}{-5}=\frac{\text{z}+3}{-5}$ and $\frac{\text{x}-8}{7}=\frac{\text{y}-7}{1}=\frac{\text{z}-5}{3}$
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