Question

If $\alpha, \beta, \gamma$ be the direction angles of a vector and $\cos \alpha=\frac{14}{15}, \cos \beta=\frac{1}{3}$, then $\cos \gamma=\ldots K \ldots$. Here, $K$ refers to

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

Answer 1

Answer: (A)

We know that,
$ l^2+m^2+n^2-1 $
$\rightarrow \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1 $
$\rightarrow \left(\frac{14}{15}\right)^2+\left(\frac{1}{3}\right)^2+\cos ^2 \gamma=1 $
$\rightarrow \frac{196}{225}+\frac{1}{9}+\cos ^2 \gamma=1 $
$\rightarrow \cos ^2 \gamma=1-\frac{196}{225}-\frac{1}{9}$
$\rightarrow \cos ^2 \gamma=\frac{225-196-25}{225}$
$\rightarrow \cos ^2 \gamma=\frac{4}{225}$
$\rightarrow^{\rightarrow} \cos ^\gamma \gamma=\pm \frac{2}{15}$