Question

Under what condition do $\bigg\langle \frac{1}{\sqrt{2}} , \frac{1}{2} , k \bigg\rangle$ represent direction cosines of a line?

• A. $ k = \frac{1}{2}$
• B. $ k = - \frac{1}{2}$
• C. $ k = \pm \frac{1}{2}$
• D. k can take any value

Answer 1

Answer: (C)

For $\left(\frac{1}{\sqrt{2}} , \frac{1}{2},k\right) $ to represent direction cosines
$\left(\frac{1}{\sqrt{2}}\right)^{2} + \left(\frac{1}{2}\right)^{2} + k^{2} = 1$
or , $ \frac{1}{2} + \frac{1}{4} + k^{2} = 1$
$ \frac{3}{4} + k^{2} = 1\Rightarrow k = \pm \frac{1}{2} $