The lines `(x-2)/(1) = (y-3)/(1) =(z-4)/(-k) and (x-3)/(k)=(y-4)/(1) = (z-5)/(1)` are coplanar if the values of k are

Options

A. `k=3` or `-3`
B. `k=0` or `-1`
C. `k=1` or `-1`
D. `k=0` or `-3`

Answer

D

Explanation

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 iff
`|(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 iff
`|(1-2,4-3,5-4),(1,1,-k),(k,2,1)|=0impliesk^(2)+3k=0impliesk=0,-3`