If the position vectors of P and Q are `hati+2hatj-7hatk and 5hati-2hatj+4hatk` respectively, the cosine of the angle between 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

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