Question

If α,β,γ be the direction angles of a vector and $\cos \alpha = \frac { 14 } { 15 }$, $\cos \beta = \frac { 1 } { 3 }$ then $\cos \gamma$=

• A. $\pm \frac { 2 } { 15 }$
• B. $\frac { 1 } { 5 }$
• C. $\pm \frac { 1 } { 15 }$
• D. None of these

Answer 1

Answer: (A)

$\pm \frac { 2 } { 15 }$

Answer 2

$\cos ^ { 2 } \alpha + \cos ^ { 2 } \beta + \cos ^ { 2 } \gamma = 1$

$\Rightarrow \cos \gamma = \sqrt { 1 - \left( \frac { 14 } { 15 } \right) ^ { 2 } - \left( \frac { 1 } { 3 } \right) ^ { 2 } }$ $= \sqrt { \frac { 8 } { 9 } - \left( \frac { 196 } { 225 } \right) } = \pm \frac { 2 } { 15 }$ .