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

Options

A. 0
B. 12
C. 16
D. 18

Answer

D

Explanation

For coplanar vectors `vec(A).(vec(B)xxvec(C))=|(A_(x),A_(y),A_(z)),(B_(x),B_(y),B_(z)),(C_(x),C_(y),C_(z))|=0`
`implies |(2,3,-2),(5,n,1),(-1,2,3)|=2(3n-2)-3(15+1)-2 (10+n)=0 implies4n-72=0implies n=18`