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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

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

B

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

C

`(16)/(sqrt(5))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
(d) According to given condition ,
`A+Bhati=Rhatj("where,R is the resukltant vector")`
Also , R=2B
`thereforeA+Bhati=2Bhatj or A=Bhatj=Bhati`
`thereforeA^(2)=4B^(2)+B^(2)=5B^(2)`
`Here, A=8`
` therefore 64=5B^(2)`
`implies B=sqrt((64)/(5))=(8)/(sqrt(5))`
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