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)`

Answer

`8/sqrt(5)`

Explanation

Angle of resultant is `90^(@)`
`:.tan analpha =sin theta/(a+b cos theta)`
`:. a+b cos theta=0` or `cos theta=-a/b`
Also given `(2a)^(2)=(8)^(2)+(a)^(2)+2ab cos theta`
`4a^(2)=64+a^(2)+2abxx (-a/b)`
`5a^(2)=64` or `a^(2)=64/5` or `a=8/sqrt(5)`