Question

If a line makes angles ${90}^{\circ },$ ${60}^{\circ }$ and ${30}^{\circ }$ with positive direction of $x,y$ and $z-$axis respectively, then direction cosines of the line respectively, are

[2 marks]

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

Answer 1

The correct option is B $0,\frac{1}{2},\frac{\sqrt{3}}{2}$

Let the direction cosines of the line be $l,m,n.$
Then, $l=\cos {90}^{\circ }=0$
$m=\cos {60}^{\circ }=\frac{1}{2}$
and $n=\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$
$(l,m,n)=(0,\frac{1}{2},\frac{\sqrt{3}}{2})$