If the straight lines x 1 y 1 z 2 k 2 and x 1 y 1 z 5 2 k are coplanar, then the plane (s) containing these two lines is (are)

Options

A. `y+2z=1`
B. `y+z=-1`
C. `y-z=-1`
D. `y-2z=-1`

Answer

B

Explanation

Since, `(x-1)/(2)=(y+1)/(k)=(z)/(2)and(x+1)/(5)=(y+1)/(2)=(z)/(k)` are coplanar.
`:.|{:(2,0,0),(2,k,2),(5,2,k):}|=0`
`rArr" "K^(2)=4" "because|{:(x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)):}|=0`
`rArr" "k=pm2`
Equation of planes containing given lines are
`|{:(x-1,y+1,z-0),(2,2,2),(5,2,2):}|=0and|{:(x-1,y+1,z-0),(2,-2,2),(5,2,-2):}|=0`
`rArr" "(x-1)(4-4)-(y+1)(4-10)+z(4-10)=0and(x-1)(4-4)-(y+1)(-4-10)+z(+10)=0`
`rArr" "6y+6-6z=0and14y+14+14z=0`
`rArr" "y-z+1=0andy+z+1=0`