Answer
$a_1 = 73.40°$
$a_2 = 64.62°$
$a_3 = 148.997°$
Work Step by Step
The direction angles are determined by the following formula:
$\cos {a_x} = \frac{u_x}{|u|}$ (from the book)
Given $u = <2, 3, -6>$
Thus $|u| = \sqrt{ 2^2 + (3)^2 + (-6)^2} = \sqrt{4 + 9 + 36} = \sqrt 49 = 7 $
$\cos a_1 = \frac{2}{7}$
$\cos a_2 = \frac{3}{7}$
$\cos a_3 = \frac{-6}{7}$
Solve for each angle.
$a_1 = 73.40°$
$a_2 = 64.62°$
$a_3 = 148.997°$
