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A vector vec(B) which has a magnitude 8....

A vector `vec(B)` which has a magnitude 8.0 is added to a vector `vec(A)` which lies along the x-axis. The sum of these two vector is a third vector which lies along the y-axis and has a magnitude that is twice the magnitude of `vec(A)`. Find the magnitude of `vec(A)`

A

`(16)/(sqrt(2))`

B

`(12)/(sqrt(5))`

C

`(6)/(sqrt(5))`

D

`(8)/(sqrt(5))`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec Q + P hati= R hatj" but "R=2P`
`therefore vec Q + Phati=2Phatj`

`therefore vec Q = 2 P hatj -P hati`
`therefore Q^(2) = 4 P^(2) +P^(2) =5P^(2)`
But magnitude of Q is 8
`therefore 8xx 8 =5P^(2)`
`therefore P^(2) =(64)/(5) therefore P =(8)/(sqrt(5))`
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