If the position vectors of `P\ a n d\ Q` are ` hat i+2 hat j-7 hat k\ a n d\ 5 hat i-3 hat j+4 hat k` them the cosine of the angle between ` vec P Q` and y-axis is `5/(sqrt(162))` b. `4/(sqrt(162))` c. `-5/(sqrt(162))` d. `(11)/(sqrt(162))`

Explanation

`vec(PQ) = vec Q – vec P`

`=5i – 3j + 4k – (i+2j-7k)`

`4i-5j+11k`

Now

`z_(com) = vec(PQ) * k`

`cos gamma = (vec(PQ) * k)/|PQ|`

`= ((3i – 5j + 11k)*k)/sqrt(4^2 + 5^2 + 11^2)`

`= 11/sqrt162`

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