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 $l=cos30°$,
$m=cos45°,n=cos60°$
$\Rightarrow l=\frac{\sqrt{3}}{2},m=\frac{1}{\sqrt{2}},n=\frac{1}{2}$