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

Page / Exercise

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

Question 1

Solution 1

Question 2

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

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

.

Question 17

Solution 17

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

Question 1

Solution 1

Question 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).

Solution 2

Question 3

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).

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

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).

Solution 6

Question 7

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

Solution 7

Question 8(i)

Solution 8(i)

Question 8(ii)

Solution 8(ii)

Question 8(iii)

Solution 8(iii)

Question 9(i)

Solution 9(i)

Question 9(ii)

Solution 9(ii)

Question 9(iii)

Solution 9(iii)

Question 9(iv)

Solution 9(iv)

Question 9(v)

Solution 9(v)

Question 9(vi)

find the angle between the following pairs of line :

Solution 9(vi)

Question 10(i)

Solution 10(i)

Question 10(ii)

Solution 10(ii)

Question 10(iii)

Solution 10(iii)

Question 10(iv)

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

Solution 10(iv)

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6(i)

Solution 6(i)

Question 6(ii)

Solution 6(ii)

Question 6(iii)

Solution 6(iii)

Question 6(iv)

Solution 6(iv)

Question 7

Solution 7

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

.

.
Question 4

Solution 4

Question 5

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.

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

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).

Solution 14

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

Question 1(i)

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

Solution 1(i)

Question 1(ii)

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

Solution 1(ii)

Question 1(iii)

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

Solution 1(iii)

Question 1(iv)

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

Solution 1(iv)

Question 1(v)

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

Solution 1(v)

Question 1(vi)

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

Solution 1(vi)

Question 1(vii)

Solution 1(vii)

Question 1(viii)

Solution 1(viii)

Question 2(i)

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

.

Solution 2(i)

Question 2(ii)

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

.

Solution 2(ii)

Question 2(iii)

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

.

Solution 2(iii)

Question 2(iv)

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

.

Solution 2(iv)

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 4(i)

Solution 4(i)

Question 4(ii)

Solution 4(ii)

Question 5

Solution 5

Question 6

Solution 6

Question 7(i)

Find the shortest distance between the lines

Solution 7(i)

Question 7(ii)

Find the shortest distance between the lines

Solution 7(ii)

Question 7(iii)

Find the shortest distance between the lines

Solution 7(iii)

Question 7(iv)

Find the shortest distance between the lines

Solution 7(iv)

Question 8

Find the distance between the lines l1 and l2 given by

Solution 8

## Chapter 28 - Straight line in space Exercise MCQ

Question 1

1. 45°
2. 30°
3. 60°
4. 90°
Solution 1

Correct option: (d)

Question 2

1. coincident
2. skew
3. intersecting
4. parallel
Solution 2

Correct option: (a)

Question 3

1. 4, 5, 7
2. 4, -5, 7
3. 4, -5, -7
4. -4, 5, 7
Solution 3

Correct option: (a)

Question 4

Solution 4

Correct option: (c)

Question 5

Solution 5

Correct option: (a)

Question 6

1. 7
2. 5
3. 0
4. none of these
Solution 6

Correct option: (a)

Question 7

Solution 7

Correct option: (c)

Question 8

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

1. -2
2. -1
3. 1
4. 2
Solution 8

Correct option: (b)

Question 9

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

Solution 9

Correct option: (a)

Question 10

Solution 10

Correct option: (b)

Question 11

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

Solution 11

Correct option: (a)

Question 12

1. parallel
2. intersecting
3. skew
4. coincident
Solution 12

Correct option: (d)

Question 13

1. parallel to x-axis
2. parallel to y-axis
3. parallel to z-axis
4. perpendicular to z-axis
Solution 13

Correct option: (d)

Question 14

Solution 14

Correct option: (d)

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

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

Solution 16

Question 17

Write the vector equaion of a line given by

Solution 17

Question 18

.

Solution 18

Question 19

Solution 19

Question 20

Solution 20

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