$$\text { The direction cosines of the vector } ( 4 \boldsymbol { i } - 8 \boldsymbol { j } + 7 \boldsymbol { k } ) \text { are: }$$
A) $( 0.35,0.81 , - 0.23 )$
B) $( 0.52,0.48 , - 0.21 )$
C) $( - 0.38,0.21 , - 0.26 )$
D) $( 0.35 , - 0.70,0.62 )$

Question

$$\text { The direction cosines of the vector } ( 4 \boldsymbol { i } - 8 \boldsymbol { j } + 7 \boldsymbol { k } ) \text { are: }$$ 
A) $( 0.35,0.81 , - 0.23 )$
B) $( 0.52,0.48 , - 0.21 )$
C) $( - 0.38,0.21 , - 0.26 )$
D) $( 0.35 , - 0.70,0.62 )$

Quizplus · Accepted Answer

The direction cosines of a vector $ \mathbf{a} = a\mathbf{i} + b\mathbf{j} + c\mathbf{k} $ are given by $ \left( \frac{a}{\sqrt{a^2 + b^2 + c^2}}, \frac{b}{\sqrt{a^2 + b^2 + c^2}}, \frac{c}{\sqrt{a^2 + b^2 + c^2}} \right) $. For the vector $ 4\mathbf{i} - 8\mathbf{j} + 7\mathbf{k} $, the direction cosines are $ \left( \frac{4}{\sqrt{4^2 + (-8)^2 + 7^2}}, \frac{-8}{\sqrt{4^2 + (-8)^2 + 7^2}}, \frac{7}{\sqrt{4^2 + (-8)^2 + 7^2}} \right) = (0.35, -0.70, 0.62) $.

The direction cosines of the vector (4i−8j+7k) are: \text { The direction cosines of the vector } ( 4 \boldsymbol { i } - 8 \boldsymbol { j } + 7 \boldsymbol { k } ) \text { are: } The direction cosines of the vector (4i−8j+7k) are:

$\text { The direction cosines of the vector } ( 4 \boldsymbol { i } - 8 \boldsymbol { j } + 7 \boldsymbol { k } ) \text { are: }$