Question

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are .

Answer 1

Consider a vector which is equally inclined to axes OX, OYand OZat angle θ, then the direction cosines of the vectors are cosθ, cosθand cosθ.

We know that,

cos 2 θ+ cos 2 θ+ cos 2 θ=1 3 cos 2 θ=1 cosθ= 1 3

So, the direction cosine of vector is 1 3 .

Hence, the direction cosines of vectors equally inclined to the axes are 1 3 , 1 3 , 1 3 .