If vec(A) = 3hat(i) + 4hat(j) and vec(B) = 7hat(i) + 24 hat(j), find a vector having the same magnitude as vec(B) and parallel to vec(A).

If vec(A) = 3hat(i) + 4hat(j) and vec(B) = 7hat(i) + 24 hat(j), find a

1.	If vec(A) = 3hat(i) + 4hat(j) and vec(B) = 7hat(i) + 24 hat(j), find a vector having the same magnitude as vec(B) and parallel to vec(A).
Answer» SOLUTION :The vector parallel to `vec(A)` and having magnitude of `vec(B)` is `vec(C) = \|vec(B)\|(vec(A))/(\|vec(A)\|) = \|vec(B)\|hat(A)` `B = SQRT(7^(2) + 24^(2)) = 25` and `hat(A) = (vec(A))/(A) = (3HAT(i) + 4hat(j))/(sqrt(3^(2) + 4^(2))) = (1)/(5)(3hat(i) + 4hat(j))` `vec(C) = 25 xx (1)/(5)(3hat(i) + 4hat(j)) = 15 hat(i) + 20 hat(j)`