Find the `(a)` scalar component and `(b)` vector component of `vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k)` on `vec(B) = hat(i) + hat(j) + hat(k)`.

Explanation

(a) Scalar component of `vec(A) along vec(B)` is
`A cos theta = vec(A) . hat(B) = ( 3 hat(i) + 4 hat(j) + 5 hat(k)). ((hat (i) + hat(j) + hat(k)))/(sqrt(3))`
` = ( 3 + 4 + 5)/(sqrt(3)) = (12)/(sqrt(3)) = 4 sqrt(3)`
(b) Vector component of `vec(A) along vec(B)` is
`(A cos theta) hat(B) = (vec(A)` . `hat(B))hat (B)`
`= (4 sqrt(3)) ((hat(i) + hat(j) + hat(k)))/(sqrt(3))`
`= 4hati+4hatj+4hat(k)`