question_answer

If the lines \[x=1+s,y=-3-\lambda s,z=1+\lambda s\] and \[x=\frac{t}{2},y=1+t,z=2-t\]are coplanar, then \[\lambda =\]

A) - 2                   

B) -1  

C)  \[-\frac{1}{2}\]            

D)  0

Correct Answer: A

Solution :

: The lines are \[\frac{x-1}{1}=\frac{y+3}{-\lambda }=\frac{z-1}{\lambda }\]and \[\frac{x}{1/2}=\frac{y-1}{1}=\frac{z-2}{-1}\] The lines are coplanar if \[\Rightarrow \]\[-1(\lambda -\lambda )-4\left( -1-\frac{\lambda }{2} \right)+1+\frac{\lambda }{2}=0\] \[\Rightarrow \]\[5+\frac{5\lambda }{2}=0\Rightarrow \lambda =-2\]