Answer
$a_1 = 65.91°$
$a_2 = 144.74°$
$a_3 = 114.09°$
Work Step by Step
The direction angles are determined by the following formula:
$\cos {a_x} = \frac{u_x}{|u|}$ (from the book)
Given $u = i - 2j - k$
Thus $|u| = \sqrt{ 1^2 + (-2)^2 + (-1)^2} = \sqrt{1 + 4 + 1} = \sqrt 6 $
$\cos a_1 = \frac{1}{\sqrt 6}$
$\cos a_2 = \frac{-2}{\sqrt 6}$
$\cos a_3 = \frac{-1}{\sqrt 6}$
Solve for each angle.
$a_1 = 65.91°$
$a_2 = 144.74°$
$a_3 = 114.09°$
