Question

Show that the direction cosines of a vector equally inclined to the axes OX, OY, and OZ are $\frac{1}{\sqrt 3}$,$\frac{1}{\sqrt 3}$,$\frac{1}{\sqrt 3}$.

Answer 1

Let a vector be equally inclined to axes OX,OY,and OZ at angle a.
Then, the direction cosines of the vector are cos a, cos a, cos a.
Now,
cos2a+cos2a+cos2a=1
$\Rightarrow$3cos2a=1
$\Rightarrow$cos a=$\frac{1}{\sqrt 3}$
Hence, the direction cosines of the vector which are equally inclined to the axes are $\frac{1}{\sqrt 3}$,$\frac{1}{\sqrt 3}$,$\frac{1}{\sqrt 3}$.