Question

$OX,OY$ are positive $X$-axis, positive $Y$-axis respectively where $O=(0,0,0)$ . The d.c.'s of the line which bisects $\angle XOY$ are

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

Answer 1

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


Equation of line bisecting XOY is $x=y$
Therefore $\alpha ={45}^0,\beta ={45}^0,\gamma ={90}^0$
$l=\cos {45}^0,m=\cos {45}^0,n=\cos {90}^0$
Hence DC's are $(\cos {45}^0,\cos {45}^0,\cos {90}^0)$
$(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},0)$