A vector `vec(A)` When added to the vector `vec(B)=3hat(i)+4hat(j)` yields a resultant vector that is in the positive y-direction and has a magnitude equal to that of `vec(B)`. Find the magnitude of `vec(A)`.

Options

A. `sqrt(10)`
B. 10
C. 5
D. `sqrt(5)`

Answer

A

Explanation

Given `vec(C )=|vec(B)|hat(j)rArr vec(C )=5hat(j)`
Let `vec(C )=vec(A)+vec(B)=vec(A)+3hat(i)+4hat(j)`
`rArr 5hat(j)=vec(A)+3hat(i)+4hat(j)`
`rArr vec(A)= -3hat(i)+hat(j) rArr |vec(A)|= sqrt(3^(2)+1^(2))=sqrt(10)`