# RD SHARMA Solutions for Class 12-science Maths Chapter 29 - The plane

Page / Exercise

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 1(v)

Solution 1(v)

Question 2

Solution 2

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 1

Solution 1

Question 2(i)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 2(iii)

Solution 2(iii)

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

## Chapter 29 - The plane Exercise Ex. 29.3

Question 1

Solution 1

Question 2(i)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 3

Solution 3

Question 4(i)

Solution 4(i)

Question 4(ii)

Solution 4(ii)

Question 4(iii)

Solution 4(iii)

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(i)

Solution 13(i)

Question 13(ii)

Solution 13(ii)

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Find the vector and Cartesian equations of the plane which passes through the point (5, 2, -4) and perpendicular to the line with direction ratios 2, 3, -1.

Solution 18

Question 19

If O be the origin and the coordinates of P be (1, 2, -3), then find the equation of the plane passing through P and perpendicular to OP.

Solution 19

Question 20

If O is the origin and the coordinates of A are (a, b, c). Find the direction cosines of OA and the equation of the plane through A at right angles to OA.

Solution 20

## Chapter 29 - The plane Exercise Ex. 29.4

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

Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin.

Solution 11

## Chapter 29 - The plane Exercise Ex. 29.5

Question 1

Solution 1

Question 2

Find the vector equation of the plane passing through the points P(2, 5, -3), Q(-2, -3, 5) and R(5, 3, -3).

Solution 2

Question 3

Solution 3

Question 4

Find the vector equation of the plane passing through the points (1, 1, -1), (6, 4, -5) and (-4, -2, 3).

Solution 4

Question 5

Solution 5

## Chapter 29 - The plane Exercise Ex. 29.6

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 2(i)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 2(iii)

Solution 2(iii)

Question 2(iv)

Solution 2(iv)

Question 2(v)

Find the angle between the planes:

2x + y - 2z = 5 and 3x - 6y - 2z = 7

Solution 2(v)

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 4(i)

Solution 4(i)

Question 4(ii)

Solution 4(ii)

Question 4(iii)

Solution 4(iii)

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

Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.

Solution 11

Question 12

Find the equation of the plane that contains the point (1, -1, 2) and is perpendicular to each of the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8.

Solution 12

Question 13

Solution 13

Question 14

Find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.

Solution 14

Question 15

Find the vector equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x - 2y + 4z = 10.

Solution 15

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 2(i)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

## Chapter 29 - The plane Exercise Ex. 29.8

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

Find the equation of the plane through the intersection of the planes 3x - y 2z = 4 and x + y + z = 2 and the point (2, 2, 1).

Solution 15

Question 16

Find the vector equation of the plane through the line of intersection of the plane x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0.

Solution 16

Question 17

Find the equation of the plane passing through (a, b, c) and parallel to the plane

Solution 17

## Chapter 29 - The plane Exercise Ex. 29.9

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

Find the distance between the point (7, 2, 4) and the plane determined by the points A (2, 5, -3), B (-2, -3, 5) and C (5, 3, -3)

Solution 11

Question 12

A plane makes intercepts -6, 3, 4 respectively on the coordinate axes. Find the length of the perpendicular from the origin on it.

Solution 12

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

## Chapter 29 - The plane Exercise Ex. 29.11

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

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 25

Find the equation of the plane passing through the points

(-1, 2, 0),(2, 2, -1) and parallel to the line

Solution 25

## Chapter 29 - The plane Exercise Ex. 29.12

Question 1(i)

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the yz-plane.

Solution 1(i)

Question 1(ii)

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the zx-plane.

Solution 1(ii)

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Find the distance of the point P (-1, -5, -10) from the point of intersection of the line joining the points A (2, -1, 2) and B (5, 3, 4) with the plane x - y + z = 5.

Solution 5

Question 6

Find the distance of the point P(3, 4,4) from the point, where the line joining the points A(3, -4, -5) and B (2, -3, 1) intersects the plane 2x + y + z =7.

Solution 6

## Chapter 29 - The plane Exercise Ex. 29.13

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

Find the equation of a plane which passes through the point (3, 2, 0) and contains the line

Solution 13

## Chapter 29 - The plane Exercise Ex. 29.14

Question 1

Solution 1

Question 2

Solution 2

Question 3

Find the shortest distance between the lines

Solution 3

## Chapter 29 - The plane Exercise Ex. 29.15

Question 1

Solution 1

Question 2

Solution 2

Question 3

Hence or otherwise deduce the length of the perpendicular.

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

Find the length and the foot of perpendicular from the point (1, 3/2, 2) to the plane 2x - 2y + 4z + 5 = 0.

Solution 14

## Chapter 29 - The plane Exercise MCQ

Question 1

The plane 2x - (1 + λ)y + 3λz = 0 passes through the intersection of the planes

1. 2x - y = 0 and y - 3z = 0
2. 2x + 3z = 0 and y = 0
3. 2x - y + 3z = 0 and y - 3z = 0
4. none of these
Solution 1

Correct option: (a)

Question 2

The acute angle between the planes 2x - y + z = 6 and x + y + 2z = 3 is

1. 45°
2. 60°
3. 30°
4. 75°
Solution 2

Correct option: (b)

Question 3

The equation of the plane through the intersection of the planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 is

1. 7x - 2y + 3z + 81 = 0
2. 23x + 14y - 9z + 48 = 0
3. 51x - 15y - 50z + 173 = 0
4. none of these
Solution 3

Correct option: (d)

Question 4

The distance between the planes 2x + 2y - z + 2 = 0 and 4x + 4y - 2z + 5 = 0 is

Solution 4

Correct option: (c)

Question 5

The image of the point (1, 3, 4) in the plane 2x - y + z + 3 = 0 is

1. (3, 5, 2)
2. (-3, 5, 2)
3. (3, 5, -2)
4. (3, -5, 2)
Solution 5

Correct option: (b)

Question 6

1. 8x + y - 5z - 7 = 0
2. 8x + y + 5z - 7 = 0
3. 8x - y - 5z - 7 = 0
4. none of these
Solution 6

Correct option: (d)

NOTE: Answer not matching with back answer.

Question 7

Solution 7

Correct option: (a)

Question 8

Solution 8

Correct option: (b)

Question 9

1. x - 5y + 3z = 7
2. x - 5y + 3z = -7
3. x + 5y + 3z = 7
4. x + 5y + 3z = -7
Solution 9

Correct option: (a)

Question 10

Solution 10

Correct option: (a)

Question 11

1. 1
2. 2
3. 3
4. none of these
Solution 11

Correct option: (c)

Question 12

1. 1
2. 2
3. 3
4. none of these
Solution 12

Correct option: (c)

Question 13

Solution 13

Correct option: (a)

Question 14

Solution 14

Correct option: (c)

Question 15

The equation of the plane parallel to the lines x - 1 = 2y - 5 = 2z and 3x = 4y - 11 = 3z - 4 and passing through the point (2, 3, 3) is

1. x - 4y + 2z + 4 = 0
2. x + 4y + 2z + 4 = 0
3. x - 4y + 2z - 4 = 0
4. none of these
Solution 15

Correct option: (a)

Question 16

1. 9
2. 13
3. 17
4. none of these
Solution 16

Correct option: (b)

Question 17

The equation of the plane through the intersection of the planes ax + by + cz + d = 0 and lx + my + nz + p = 0 and parallel to the line y = 0, z = 0

1. (bl - am)y + (cl - an)z + dl - ap = 0
2. (am - bl)x + (mc - bn)z + md - bp = 0
3. (na - cl)x + (bn - cm)y + nd - cp = 0
4. none of these
Solution 17

Correct option: (a)

Question 18

The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is

1. x + y + z = 1
2. x + y + z = 0
3. x + y - z = 1
4. x + y + z = 2
Solution 18

Correct option: (a)

## Chapter 29 - The plane Exercise Ex. 29VSAQ

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

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Find the length of the perpendicular drawn from the origin to the plane 2x - 3y + 6z + 21 = 0.

Solution 19

Question 20

Solution 20

Question 21

Solution 21

### STUDY RESOURCES

REGISTERED OFFICE : First Floor, Empire Complex, 414 Senapati Bapat Marg, Lower Parel, Mumbai - 400013, Maharashtra India.
Copyright Notice © 2021 Greycells18 Media Limited and its licensors. All rights reserved.