If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to and

Question

Philoid · Accepted Answer

Given: vectors are mutually perpendicular to each other and are of equal magnitude.

And

Let the vector be inclined to at angles α, β and γ respectively.

Then, we have

From (1), (2) and (3)

As

Hence,

Hence, the vector are equal inclined to .