Question

If the d.c's of a line are $\left(\frac{1}{c},\frac{1}{c},\frac{1}{c}\right)$, find c.

Answer 1

d.c's line $\to \frac{1}{c},\frac{1}{c},\frac{1}{c}$

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

$\frac{1}{c^2}+\frac{1}{c^2}+\frac{1}{c^2}=1$

$\frac{3}{c^2}=1$

$c^2=3$

$c=\pm \sqrt{3}$

the value of c is $\pm \sqrt{3}$