Question

A line with direction cosines proportional to 2,1, 2 meets each of the lines and . The co-ordinates of each of the points of intersection are given by
[AIEEE 2004]

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

Let the two lines be AB and CD having equation $\frac{x}{1}=\frac{y+a}{1}=\frac{z}{1}=\lambda$ and $\frac{x+a}{2}=\frac{y}{1}=\frac{z}{1}=\mu$
then $P\equiv (\lambda ,\lambda ,-a,\lambda )$ and $Q=(2\mu ,-a,\mu ,\mu )$
So according to question,
$\frac{\lambda -2\mu }{2}=\frac{\lambda -a-\mu }{1}=\frac{\lambda -\mu }{2}$

$\Rightarrow \mu =aand\lambda =3a$
$\therefore$ P $\equiv$ (3a,2a,3a) and Q $\equiv$ (a,a,a).