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If the straight linesx 1 y 1 z 2 k 2andx 1 y 1 z 5 2 kare coplanar, then the plane (s)containing these two lines is (are) (A) y + 2z = 1 (B) y + z = 1 (C) y z = 1 (D) y 2z = 1 55A. `y+2z=-1`B. `y+z=-1`C. `y-z=-1`D. `y-2z=-1`

Answer» Correct Answer - B::C
PLAN If the straight lines are coplanar. They the should lie in same plane.
Description of Situation If straight lines are coplanar.
`implies" "|{:(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`
Since,`" "(x-1)/(2)=(y+1)/(K)=(z)/(2)`
and`" "(x+1)/(5)=(y+1)/(2)=(z)/(k)` are coplanar.
`implies" "|{:(2,0,0),(2,K,2),(5,2,K):}|=0impliesK^(2)=4impliesK=+-2`
`:." "n_(1)=b_(1)xxd_(1)=6j-6k," for "k=2`
`:." "n_(2)=b_(2)xxd_(2)=14j-14k," for "k=-2`
So, equation of planes are `(r-a).n_(1)=0`
`implies" "y-z=-1" and "(r-a).n_(2)=0`
`implies" "y+z=-1`


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