Answer
$a_1 = 64.89 degrees$
$a_2 = 55.55 degrees$
$a_3 = 45 degrees$
Work Step by Step
The direction angles are determined by the following formula:
$\cos {a_x} = \frac{u_x}{|u|}$ (from the book)
Given $u = 3i + 4j + 5k$
Thus $|u| = \sqrt{ 3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt 50 = 5\sqrt2$
$\cos a_1 = \frac{3}{5\sqrt2}$
$\cos a_2 = \frac{4}{5\sqrt2}$
$\cos a_3 = \frac{5}{5\sqrt2}$
Solve for each angle.
$a_1 = 64.8959°$
$a_2 = 55.5501°$
$a_3 = 45°$
