Find the direction cosines of the vector u given below. $$\mathbf { u } = 4 \mathbf { i } + 4 \mathbf { j } + 5 \mathbf { k }$$
A)
$\cos ( \alpha ) = \frac { 16 } { \sqrt { 57 } } , \cos ( \beta ) = \frac { 16 } { \sqrt { 57 } } , \cos ( \gamma ) = \frac { 25 } { \sqrt { 57 } }$
B)
$\cos ( \alpha ) = \frac { - 8 } { \sqrt { 57 } } , \cos ( \beta ) = \frac { - 8 } { \sqrt { 57 } } , \cos ( \gamma ) = \frac { - 10 } { \sqrt { 57 } }$
C)
$\cos ( \alpha ) = \frac { 4 } { \sqrt { 57 } } , \cos ( \beta ) = \frac { 4 } { \sqrt { 57 } } , \cos ( \gamma ) = \frac { 5 } { \sqrt { 57 } }$
D)
$\cos ( \alpha ) = \frac { 8 } { \sqrt { 57 } } , \cos ( \beta ) = \frac { 8 } { \sqrt { 57 } } , \cos ( \gamma ) = \frac { 10 } { \sqrt { 57 } }$
E)
$\cos ( \alpha ) = \frac { - 4 } { \sqrt { 57 } } , \cos ( \beta ) = \frac { - 4 } { \sqrt { 57 } } , \cos ( \gamma ) = \frac { - 5 } { \sqrt { 57 } }$

Question

Quizplus · Accepted Answer

The direction cosines of a vector $	extbf{u} = a	extbf{i} + b	extbf{j} + c	extbf{k}$ are given by $\cos(\alpha) = \frac{a}{|	extbf{u}|}, \cos(\beta) = \frac{b}{|	extbf{u}|},$ and $\cos(\gamma) = \frac{c}{|	extbf{u}|}$. In this case, $|	extbf{u}| = \sqrt{4^2+4^2+5^2} = \sqrt{57}$, and so we have $$\cos(\alpha) = \frac{4}{\sqrt{57}}, \quad \cos(\beta) = \frac{4}{\sqrt{57}}, \quad 	ext{and} \quad \cos(\gamma) = \frac{5}{\sqrt{57}}.$$ Therefore, the answer is $\boxed{	ext{(C)}}.$

Find the Direction Cosines of the Vector U Given Below u=4i+4j+5k\mathbf { u } = 4 \mathbf { i } + 4 \mathbf { j } + 5 \mathbf { k }u=4i+4j+5k

Find the Direction Cosines of the Vector U Given Below $\mathbf { u } = 4 \mathbf { i } + 4 \mathbf { j } + 5 \mathbf { k }$