# RBSE Solutions for Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.7

## Rajasthan Board RBSE Class 12 Maths Chapter 14 Three Dimensional Geometry Ex 14.7

Question 1.
Find the angle between the planes :

Solution:

Question 2.
Find the angle between the planes :
(i) x + y + 2z = 9 and 2x – y + z = 15
(ii) 2 x – y + z = 4 and x + y + 2z = 3
(iii) x + y – 2z = 3 and 2x – 2y + z = 5
Solution:
If plane are a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0 then angle between them is

Question 3.
Show that following planes are at right angles :

Solution:
x – 2y + 4z = 10 and 18x + 17y + 4z = 49
a1 = 1,b1 = -2, c1 = 4 and a2 = 18 b2 = 17, c2 = 4

(i) Planes will be perpendicular if
a1 a2 + b1b2 + c1c2 = 0
L.H.S. = 1 × 18 + (-2) × 17 + 4 × 4
= 18 – 34+16
= – 34 + 34
= 0
∴ L.H.S. = R.H.S.

Question 4.
Find λ, if following planes are perpendicular to each other:

Solution:

Question 5.
Find the angle between the line $$\frac { x+1 }{ 3 }$$ = $$\frac { y-1 }{ 2 }$$ = $$\frac { z-2 }{ 4 }$$ and the plane 2x + y – 3z + 4 = 0
Solution:
Normal vector of the plane 2x + y – 3z + 4 = 0

Question 6.
Find the ngle between the line $$\frac { x-2 }{ 3 }$$ = $$\frac { y+1 }{ -1 }$$ = $$\frac { z-3 }{ 2 }$$ and the plane 3x + 4y + z + 5 = 0.
Solution:

Question 7.
Find the angle between

Solution:
We know that the angle between the line and the plane is

Question 8.
Find the angle between

Solution:
We know that angle between the line

Question 9.
Determine the value of m, if line

Solution:

Question 10.
Find m, if line

is parallel to the plane

Solution:
If given line is parallel to given plane