If a→,b→ and c→  are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is

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→|cos⁡θ=|a→|or  cos⁡θ=1|α→|Similarly, cos⁡ϕ=1|α→|,cos⁡ψ=1|α→|