Find the directional consines of vector `(5hati+2hatj+6hatk)`. Also write the value of sum of squares of directional cosines of this vector.

Explanation

Let `alpha, beta & lambda` are the angles of vector `(5hati+2hatj+6hatk)` from x,y `&` z-axis respectively.
then `cos alpha=(A_(x))/(A)=(6)/(|5hati+2hatj+6hatk|)=(6)/sqrt(65)`
`cos gamma=(A_(z))/(A)=(6)/(|55hati+2hatj+6hatk|)=(6)/sqrt(65)`
The sum of squares of directional cosines of this vector `cos^(2)alpha+cos ^(2) beta+cos ^(2) gamma=(5^(2)+2^(2)+6^(2))/(65)=(65)/(65)=1`