Question

The direction cosines of a line are k, k, k, then
(a) k > 0
(b) 0 < k < 1
(c) k = 1
(d) $k=\frac{1}{\sqrt{3}}\mathrm{or}-\frac{1}{\sqrt{3}}$

Answer 1

Given direction cosines of a line are k, k and k.
Say l = k, m = k, n = k
Since direction cosines are such that
l² + m² + n² = 1
∴ k² + k² + k² = 1
i.e 3k² = 1
i.e k_² = $\frac{1}{3}$
$\mathrm{i}.\mathrm{e}k=\pm \frac{1}{\sqrt{3}}$

Hence, the correct answer is option D.