Question

Find the direction angles of vector $-8\hat{i}+3\hat{j}+2\hat{k}$.

• A. ${156}^o,{70}^o,{77}^o$
• B. ${155}^o,{72}^o,{80}^o$
• C. ${145}^o,{83}^o,{74}^o$
• D. ${150}^o,{76}^o,{83}^o$

Answer 1

The correct option is A ${156}^o,{70}^o,{77}^o$

$\overrightarrow{a}=-8\hat{i}+3\hat{j}+2\hat{k}\cos \alpha =\frac{-8}{\sqrt{{(-8)}^2+{\left(3\right)}^2+{\left(2\right)}^2}}=\frac{-8}{\sqrt{77}}=-.91\Rightarrow \alpha ={\cos }^{-1}(-.91)={156}^{\circ }\cos \beta =\frac{3}{\sqrt{{(-8)}^2+{\left(3\right)}^2+{\left(2\right)}^2}}=\frac{3}{\sqrt{77}}=.34\Rightarrow \beta ={\cos }^{-1}\left(.34\right)={70}^{\circ }\cos \gamma =\frac{2}{\sqrt{{(-8)}^2+{\left(3\right)}^2+{\left(2\right)}^2}}=\frac{2}{\sqrt{77}}=.23\Rightarrow \gamma ={\cos }^{-1}\left(.23\right)={77}^{\circ }$

So the direction angles are ${156}^{\circ },{70}^{\circ },{77}^{\circ }$

Option $A$ is correct.