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A vector vec P when added to the sum of ...

A vector `vec P` when added to the sum of the vectors `2hati-3hatj+hatk and -3hati-hatj+hatk` gives a unit vector along the x-axis. What is the magnitude of the vector `vec P` ?

A

`sqrt(12)`

B

`sqrt(20)`

C

`sqrt(24)`

D

`sqrt(32)`

Text Solution

Verified by Experts

The correct Answer is:
C
Unit vector along x-axis means `hati`. Let P be the required vector. Then, `2hati-3hatj+hatk+(-3hati)-hatj+hatk+vec P=hati`
`vec P =(hati-2hati+3hati)+(3hatj+hatj)-hatk-hatk`
`therefore vec P =2hati+4hatj-2hatk`
`therefore P_(x) =2, P_(y)=4 and P_(z)=-2`
`therefore` Magnitude of `P =sqrt(2^(2)+4^(2)+(-2)^(2))`
`=sqrt(4+16+4)=sqrt(24)`
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