If `vec(A)=2hati + 3hatj` and `vec(B)=hati + hatj`, then the vector component of `vec(A)` in the direction of `vec(B)` is :

Options

A. `(hati + hatj)`
B. `2.5(hati + hatj)`
C. `2(hati + hatj)`
D. `3(hati + hatj)`

Answer

B

Explanation

Here component of A in the direction of `vec(B)` is
`Acostheta=((Acostheta)B)/B`
`=(ABcostheta)/B=(vec(A).vec(B))/B=(vec(A)vec(B))/B(vec(B)/B)`
`=5/sqrt(2)(hati+hatj)/sqrt(2)=2.5(hati+hatj)`