If the straight lines `x=-1+s ,y=3-lambdas ,z=1+lambdasa n dx=t/2,y=1+t ,z=2-t ,` with paramerters `sa n dt ,` respectivley, are coplanar, then find `lambdadot`

Options

A. `0`
B. `-1`
C. `-1/2`
D. `-2`

Answer

D

Explanation

Given lines are
`(x-1)/1=(y+3)/(-lamda)=(z-1)/(lamda)=s` and `(x-0)/(1//2)=(y-1)/1=(z-2)/(-1)=t`
We know that the lines
`(x-x_(1))/(l_(1))=(y-y_(1))/(m_(1))=(z-z_(1))/(n_(1))` and `(x-x_(2))/(l_(2))=(y-y_(2))/(m_(2))=(z-z_(2))/(n_(2))`
are coplanar, if
`|(x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2))|=0`
So the given lines will be coplanar, if
`|(0-1,1-(-3),2-1),(1,-lamda,lamda),(1//2,1,-1)|=0implieslamda=-2`