Question

If the two directional cosines of a vectors are $\frac{1}{\sqrt{2}}$ and $\frac{1}{\sqrt{3}}$ then the value of third directional cosines is

• A. $\frac{1}{\sqrt{6}}$
• B. $\frac{1}{\sqrt{5}}$
• C. $\frac{1}{\sqrt{7}}$
• D. $\frac{1}{\sqrt{10}}$

Answer 1

The correct option is A $\frac{1}{\sqrt{6}}$

we have,

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

${\left(\frac{1}{\sqrt{2}}\right)}^2+{\left(\frac{1}{\sqrt{3}}\right)}^2+{\cos }^2\gamma =1$

${\cos }^2\gamma =1-\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$

$\therefore \cos \gamma =\frac{1}{\sqrt{6}}$