If a→,b→ and c→ are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is
a→+b→+c→
a→|a→|+b→|b→|+c→|c→|
a→|a→|2+b→|b→|2+c→|c→|2
|a→|a→−|b→|b→+|c→|c→
Let α→=a→|a→|+b→|b→|+c→|c→|
Since a→,b→ and c→ are mutually perpendicular vectors, if α→makes angles θ,ϕ,ψ with a→,b→ and c→ respectively, thenα→⋅a→=a→⋅a→|a→|or |α→|⋅|a→|cosθ=|a→|or cosθ=1|α→|
Similarly, cosϕ=1|α→|,cosψ=1|α→|