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

## Chapter 29 - The plane Exercise Ex. 29.1

## Chapter 29 - The plane Exercise Ex. 29.2

## Chapter 29 - The plane Exercise Ex. 29.3

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.

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*.

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.

## Chapter 29 - The plane Exercise Ex. 29.4

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

## Chapter 29 - The plane Exercise Ex. 29.5

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

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

## Chapter 29 - The plane Exercise Ex. 29.6

Find the angle between the planes:

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

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

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.

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.

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.

## Chapter 29 - The plane Exercise Ex. 29.7

## Chapter 29 - The plane Exercise Ex. 29.8

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).

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.

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

## Chapter 29 - The plane Exercise Ex. 29.9

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)

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

## Chapter 29 - The plane Exercise Ex. 29.10

## Chapter 29 - The plane Exercise Ex. 29.11

Find the equation of the plane passing through the points

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

## Chapter 29 - The plane Exercise Ex. 29.12

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

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

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.

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.

## Chapter 29 - The plane Exercise Ex. 29.13

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

## Chapter 29 - The plane Exercise Ex. 29.14

Find the shortest distance between the lines

## Chapter 29 - The plane Exercise Ex. 29.15

Hence or otherwise deduce the length of the perpendicular.

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

## Chapter 29 - The plane Exercise MCQ

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

- 2x - y = 0 and y - 3z = 0
- 2x + 3z = 0 and y = 0
- 2x - y + 3z = 0 and y - 3z = 0
- none of these

Correct option: (a)

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

- 45°
- 60°
- 30°
- 75°

Correct option: (b)

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

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

Correct option: (d)

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

Correct option: (c)

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

- (3, 5, 2)
- (-3, 5, 2)
- (3, 5, -2)
- (3, -5, 2)

Correct option: (b)

- 8x + y - 5z - 7 = 0
- 8x + y + 5z - 7 = 0
- 8x - y - 5z - 7 = 0
- none of these

Correct option: (d)

NOTE: Answer not matching with back answer.

Correct option: (a)

Correct option: (b)

- x - 5y + 3z = 7
- x - 5y + 3z = -7
- x + 5y + 3z = 7
- x + 5y + 3z = -7

Correct option: (a)

Correct option: (a)

- 1
- 2
- 3
- none of these

Correct option: (c)

- 1
- 2
- 3
- none of these

Correct option: (c)

Correct option: (a)

Correct option: (c)

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

- x - 4y + 2z + 4 = 0
- x + 4y + 2z + 4 = 0
- x - 4y + 2z - 4 = 0
- none of these

Correct option: (a)

- 9
- 13
- 17
- none of these

Correct option: (b)

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

- (bl - am)y + (cl - an)z + dl - ap = 0
- (am - bl)x + (mc - bn)z + md - bp = 0
- (na - cl)x + (bn - cm)y + nd - cp = 0
- none of these

Correct option: (a)

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

- x + y + z = 1
- x + y + z = 0
- x + y - z = 1
- x + y + z = 2

Correct option: (a)

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

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

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