Lines x-21=y-31=z-4-k and x-1k=y-42=z-51 are coplanar, if
k=2
k=0
k=3
k=-1
Explanation of the correct option:
Finding the value of k:
Compare x-21=y-31=z-4-k with [x-x1]a1=[y-y1]b1=[z-z1]c1.
Therefore, x1=2,y1=3,z1=4,a1=1,b1=1,c1=-k.
Similarly, compare x-1k=y-42=z-51with [x-x2]a2=[y-y2]b2=[z-z2]c2.
Hence, x2=1,y2=4,z2=5,a2=k,b2=2,c2=1
.Lines are coplanar if |x2-x1y2-y1z2-z1a1b1c1a2b2c2|=0
⇒-11111-kk21=0⇒-(1+2k)-1(1+k2)+1(2-k)=0⇒-1-2k-1-k2+2-k=0⇒k2+3k=0⇒k=0,k=-3
Hence, the correct answer is option (B)