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If the position vectors of P and Q are h...

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

A

`(4)/(sqrt(162))`

B

`(11)/(sqrt(162))`

C

`(5)/(sqrt(162))`

D

`(-5)/(sqrt(162))`

Text Solution

Verified by Experts

The correct Answer is:
B
`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.
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