Given : equations of perpendicular planes-

2x – 5y + kz = 4

x + 2y – z = 6

To Find : k

Formulae :

Normal vector to the plane :

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

Vector normal to the plane is given by,

Answer :

For given planes –

2x – 5y + kz = 4

x + 2y – z = 6

normal vectors are

As given vectors are perpendicular, hence their normal vectors are also perpendicular to each other.

(2×1) + (-5×2) + (k×(-1)) = 0

2 – 10 – k = 0

- 8 – k = 0

k = -8