Question

A straight line makes an angle of $ 30^° $ , $ 45^° $ and $ 60^° $ with the positive direction of $ X $ - axis, $ Y $ - axis and $ Z $ - axis respectively. What are the direction cosines of the straight line?

• A. $ \frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{\sqrt{3}}{2} $
• B. $ 0, \frac{1}{\sqrt{2}}, \frac{1}{2} $
• C. $ \frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}, \frac{1}{2} $
• D. $ \frac{1}{\sqrt{2}},\frac{\sqrt{3}}{2}, 1 $

Answer 1

Answer: (C)

Let direction cosines of a line making angle $\alpha$ with $X-$axis, $\beta$ with $Y$-axis and $\gamma$ with $Z$-axis are $l, m, n$.
$\therefore l = cos \,\alpha, m = cos \,\beta \,n = cos\, \gamma$
Given, $\alpha = 30°, \beta = 45°$ and $\gamma = 60°$
$\therefore $ Direction cosines of the line are $l = cos \,30°$,
$m = cos \,45°, n = cos \,60°$
$\Rightarrow l = \frac{\sqrt{3}}{2}, m = \frac{1}{\sqrt{2}}, n = \frac{1}{2}$