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

If the position vectors of P and Q are i + 3j - 7k and 5i - 2j + 4k then the cosine of the angle between PQ and y - 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
`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.
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