If the position vectors of P and Q are `hati+2hatj-7hatk` and `5hati-3hatj+4hatk` respectively, the cosine of the angle between `vec(PQ)` and z-axis is

Options

A. `4/sqrt(162)`
B. `11/sqrt(162)`
C. `5/sqrt(162)`
D. `-5/sqrt(162)`

Answer

B

Explanation

`vec(PQ)=vec(OQ) - vec(OP) = 4hati-5hatj+11hatk`
`therefore (vec(PQ))/(|vec(PQ)|)= 4/sqrt(162) hati - 5/sqrt(162)hatj + 11/sqrt(162)hatk`
`therefore coslambda=11/sqrt(162)`, where `lambda` is the angle of `vec(PQ)` with z-axis.