Show that the vector `hat(i) +hat(j)+hat(k)` is equally inclined to the axes OX,OY and OZ.

Explanation

Let `a=hat(i)+hat(j)+hat(k)`.
Then ,magnitude of vector `a=|a|=sqrt(1^2+1^2+1^2)=sqrt(3)`
Therefore , the direction consines of are `(x).(|a|),(y)/(|a|),(z)/(|a|) i.e.,(1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3))`.
If a makes angles a,b and r respectively with (postive) OX,OY and OZ.
Then , we have `cos alpha =1 sqrt(3)`.
(`because` Direction cosines are the cosines of the angles made by `hat(i),hat(j),hat(k)` components of the vector with X,Y and Z axes)
`cos beta=(1)/(3) and cos gamma =(1)/(3),alpha=beta=gamma=cos^(-1)((1)/(sqrt(3)))`.