If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$, then…
If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$, then $c$ is equal to
- $\pm \sqrt{2}$
- $\pm \sqrt{3}$
- $\pm 2$
- $\pm 3$
Solution
Direction cosine of line is $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$.
$\therefore \quad \frac{1}{c^2}+\frac{1}{c^2}+\frac{1}{c^2}=1$
$\Rightarrow \quad \frac{3}{c^2}=1 \Rightarrow c^2=3$
$\therefore \quad c= \pm \sqrt{3}$
Asked in: AP EAMCET 2021 (24 Aug Shift 2)
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