Find the angle between the planes 2x + y – 2z = 5 and 3x – 6y – 2z = 7.

Question

Philoid · Accepted Answer

Given : equations of planes-

2x + y – 2z = 5

3x – 6y – 2z = 7

To Find : angle between two planes

Formulae :

1) Normal vector to the plane :

If equation of the plane is ax + by + cz = d then,

Vector normal to the plane is given by,

2) Angle between two planes :

The angle Ө between the planes and is given by

Answer :

For given planes

2x + y – 2z = 5

3x – 6y – 2z = 7

Normal vectors are

and

Therefore, angle between two planes is