Choose the one alternative that best completes the statement or answers the question.
Find the direction angles of the vector. Round to the nearest degree, if necessary.
-$$\mathbf { v } = - 6 \mathbf { i } - 4 \mathbf { j } - 12 \mathbf { k }$$
A) $\alpha = 117 ^ { \circ } , \beta = 108 ^ { \circ } , \gamma = 157 ^ { \circ }$
B) $\alpha = 115 ^ { \circ } , \beta = 107 ^ { \circ } , \gamma = 149 ^ { \circ }$
C) $\alpha = 118 ^ { \circ } , \beta = 108 ^ { \circ } , \gamma = 161 ^ { \circ }$
D) $\alpha = 92 ^ { \circ } , \beta = 91 ^ { \circ } , \gamma = 94 ^ { \circ }$

Question

Quizplus · Accepted Answer

The direction angles are calculated using the formulas: $\cos \alpha = \frac{-6}{14}$, $\cos \beta = \frac{-4}{14}$, $\cos \gamma = \frac{-12}{14}$. Solving these gives $\alpha \approx 115^\circ$, $\beta \approx 107^\circ$, $\gamma \approx 149^\circ$.

Choose the One Alternative That Best Completes the Statement or Answers