The projection of the vector `vec(A)= hat(i)-2hat(j)+hat(k)` on the vector `vec(B)= 4hat(i)-4hat(j)+7hat(k)` is

Options

A. `(19)/9`
B. `(38)/9`
C. `8/9`
D. `4/9`

Answer

A

Explanation

Here, `vec(A)= hat(i)-2hat(j)+hat(k)`
`vec(B)= 4hat(i)-4hat(j)+7hat(k)`
The projection of `vec(A)` on `vec(B)= A cos theta`
`A cos theta= (AB cos theta)/B= (vec(A).vec(B))/B`
`=((hat(i)-2hat(j)+hat(k)).(4hat(i)-4hat(j)+7hat(k)))/(sqrt((4)^(2)+(-4)^(2)+(7)^(2)))`
`=(4+8+7)/(sqrt(18))=(19)/9`