Question

In a line $OP$ through the origin $O$ makes angles of ${90}^{\circ },{60}^{\circ }and{60}^{\circ }$ with $x,y$ and $z$ axis respectively then the direction cosines of $OP$ are

• A. $\left(A\right)\frac{1}{2},\frac{1}{\sqrt{2}},\frac{\sqrt{3}}{2}$
• B. $\left(B\right)\sqrt{2},2\sqrt{6}$
• C. $\left(C\right)\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}},\frac{1}{2}$
• D. None of these

Answer 1

Answer: (D)

None of these

We know that ,

The direction cosines of a line making angle $\alpha$ with x-axis, $\beta$ with y- axis and $\gamma$ with z-axis are $l,m,n.$

Then,

$l=\cos \alpha ,m=\cos \beta ,n=\cos \gamma$

Given that $\alpha ={90}^0,\beta ={60}^{0}and\gamma ={60}^0$

So, direction cosines of a line

$l=\cos {90}^0,m=\cos {60}^0,n=\cos {60}^0$

$l=0,m=\frac{1}{2},n=\frac{1}{2}$

Therefore direction cosines are $(0,\frac{1}{2},\frac{1}{2})$.

Option (D) is correct answer.