# RD SHARMA Solutions for Class 12-science Maths Chapter 28 - Straight line in space

## Chapter 28 - Straight line in space Exercise Ex. 28.1

Find the vector equation of the line passing through the points (-1, 0, 2) and (3, 4, 6).

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## Chapter 28 - Straight line in space Exercise Ex. 28.2

Show that the line through the points (1, -1, 2) and (3, 4, -2) is perpendicular to the line through points (0, 3, 2) and (3, 5, 6).

Show that the line through the points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (-1, -2, 1) and (1, 2, 5).

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).

Find the equation of a line parallel to x-axis and passing through the origin.

find the angle between the following pairs of line :

find the angle between the pairs of lines with directions ratios proposal to a, b, c and b - c, c - a, a - b.

## Chapter 28 - Straight line in space Exercise Ex. 28.3

## Chapter 28 - Straight line in space Exercise Ex. 28.4

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Find the foot of perpendicular from the point (2, 3, 4) to the line . Also find the perpendicular distance from the given point to the line.

Find the coordinates of the foot of perpendicular drawn from the point A (1, 8, 4) to the line joining the points B (0, -1, 3) and C (2, -3, -1).

## Chapter 28 - Straight line in space Exercise Ex. 28.5

Find the shortest distance between the pair of lines whose vector equation are

Find the shortest distance between the pair of lines whose vector equations are:

Find the shortest distance between the pair of lines whose vector equations are:

Find the shortest distance between the lines whose vector equations are:

Find the shortest distance between the pair of lines whose vector equations are:

Find the shortest distance between the pair of lines whose vector equations are:

Find the shortest distance between the pair of lines whose cartesian equations are:

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Find the shortest distance between the pair of lines whose cartesian equations are:

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Find the shortest distance between the pair of lines whose cartesian equations are:

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Find the shortest distance between the pair of lines whose Cartesian equations are:

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Find the shortest distance between the lines

Find the shortest distance between the lines

Find the shortest distance between the lines

Find the shortest distance between the lines

Find the distance between the lines *l*_{1 }and *l*_{2} given by

## Chapter 28 - Straight line in space Exercise MCQ

- 45°
- 30°
- 60°
- 90°

Correct option: (d)

- coincident
- skew
- intersecting
- parallel

Correct option: (a)

- 4, 5, 7
- 4, -5, 7
- 4, -5, -7
- -4, 5, 7

Correct option: (a)

Correct option: (c)

Correct option: (a)

- 7
- 5
- 0
- none of these

Correct option: (a)

Correct option: (c)

If a line makes angles α, β and γ with the axes respectively, then cos 2 α + cos 2 β + cos 2 γ =

- -2
- -1
- 1
- 2

Correct option: (b)

NOTE: Answer not matching with back answer.

If the direction ratios of a line are proportional to 1, -3, 2, then its direction cosines are

Correct option: (a)

Correct option: (b)

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

Correct option: (a)

- parallel
- intersecting
- skew
- coincident

Correct option: (d)

NOTE: Answer not matching with back answer.

- parallel to x-axis
- parallel to y-axis
- parallel to z-axis
- perpendicular to z-axis

Correct option: (d)

Correct option: (d)

## Chapter 28 - Straight line in space Exercise Ex. 28VSAQ

If the equations of a line *AB* are , write the direction ratios of a line parallel to *AB*.

Write the vector equaion of a line given by

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