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You are given a vector, vec P =(1)/(sq...

You are given a vector,
`vec P =(1)/(sqrt(2)) cos theta hati+(1)/(sqrt(2)) sin theta hatj` What is the unit vector in the direction of `vec P` ?

A

`(1)/(sqrt(2)) [cos theta hati+sin theta hatj]`

B

`cos theta hati+ sin theta hatj`

C

`cos theta hati- sin theta hatj`

D

`(1)/(2) [cos theta hati- sin theta hatj]`

Text Solution

Verified by Experts

The correct Answer is:
B
The unit vector in the direction of `vec P` is
`hat n =(vec P)/(|vec P|) =(vec P)/(P)`
`|vec P| = sqrt (((1)/(sqrt(2))cos theta )^(2) + ((1)/(sqrt(2)) sin theta )^(2))`
`=sqrt((1)/(2) (cos^(2) theta + sin^(2) theta)) =(1)/(sqrt(2))`
`therefore hatn =(vec P)/(P)=((1)/(sqrt(2)) cos theta hati +(1)/(sqrt(2)) sin theta hatj)/((1)/(sqrt(2)))`
`therefore hatn = cos theta hati + sin theta hatj`
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