Question

If vector a, vector b and vector c  are mutually perpendicular vectors of equal magnitudes, show that the vector vector (a + b + c) is  equally inclined to vector a, vector b and vector c.

Answer 1

Given that vector a, vector b and vector c  are mutually perpendicular vectors

∴ vector(a x b) = vector(b x c) = vector (c x a) = 0

It is also given that |vector a| = |vector b| = |vector c|

Let vector vector(a + b + c)  be inclined to vector a, vector b and vector c  at angles α, β and γ respectively

Now as |vector a| = |vector b| = |vector c|,  therefore, cosα = cosβ = cosγ

∴ α = β = γ

Hence, the vector(a + b + c) is s equally inclined to vector a, vector b and vector c.