Question

If $\alpha ,\beta ,\gamma$ be the direction angles of a vector and $\cos \alpha =\frac{14}{15},\cos \beta =\frac{1}{3}$, then $\cos \gamma =\dots K\dots$. 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,
$l^2+m^2+n^2-1$
$\to {\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$
$\to {\left(\frac{14}{15}\right)}^2+{\left(\frac{1}{3}\right)}^2+{\cos }^2\gamma =1$
$\to \frac{196}{225}+\frac{1}{9}+{\cos }^2\gamma =1$
$\to {\cos }^2\gamma =1-\frac{196}{225}-\frac{1}{9}$
$\to {\cos }^2\gamma =\frac{225-196-25}{225}$
$\to {\cos }^2\gamma =\frac{4}{225}$
${\to }^{\to }{\cos }^{\gamma }\gamma =\pm \frac{2}{15}$