Question

Show that the following planes are at right angles:

(i) vector r.(4i - 7j - 8k) = 5 and vector r.(3i - 4j + 5k) + 10 = 0 

(ii) vector r.(2i + 6j + 6k) = 13 and vector r.(3i + 4j - 5k) + 7 = 0

Answer 1

(i) We know that

Therefore, it is proved that the planes are at right angles.

(ii) We know that

On further calculation

= 6 + 24 – 30

= 30 – 30 = 0 = RHS

Therefore, it is proved that the planes are at right angles.