The lines `(x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1` are coplanar if a. `k=1or-1` b. `k=0or-3` c. `k=3or-3` d. `k=0or-1`

Options

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

Answer

b

Explanation

The lines `(x-2)/(1)=(y-3)/(1)=(z-4)/(-k)" "(i)`
and `(x-1)/(k)=(y-4)/(2)=(z-5)/(1)" "(ii)`
are coplanar if `|[x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)],[l_(1),m_(1),n_(1)],[l_(2),m_(1),n_(2)]|=0`
or `|[1,-1,-1],[1,1,-k],[k,2,1]|=0`
or `k^(2)+3k=0`
`impliesk=0or-3`