Question

Find a unit vector in the direction of u and in the direction opposite that of u. u = (−4, 2, 5)

(a) in the direction of u
(b) in the direction opposite that of u

Answer 1

To find a unit vector in the direction of u, divide u by its magnitude. To find a unit vector in the opposite direction of u, change the signs of the components of the unit vector in the direction of u.

Step-by-step explanation:

To find a unit vector in the direction of u, you need to divide u by its magnitude. The magnitude of u is given by |u| = sqrt((-4)^2 + 2^2 + 5^2). So, |u| = sqrt(16 + 4 + 25) = sqrt(45). A unit vector in the direction of u is u/|u| = (-4/sqrt(45), 2/sqrt(45), 5/sqrt(45)).

To find a unit vector in the opposite direction of u, you simply change the signs of the components of the unit vector in the direction of u. So, a unit vector in the opposite direction of u is (-(-4/sqrt(45)), -(2/sqrt(45)), -(5/sqrt(45))) = (4/sqrt(45), -2/sqrt(45), -5/sqrt(45)).