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If the straight lines (x-1)/(2)=(y+1)/(l...

If the straight lines `(x-1)/(2)=(y+1)/(lamda)=(z)/(2)and(x+1)/(5)=(y+1)/(2)=(z)/(lamda)` are coplanar, find `lamda` and equations of the planes containing theses two lines.

A

`y+2z=-1`

B

`y+z=-1`

C

`y-z=-1`

D

`y-2z=-1`

Text Solution

Verified by Experts

The correct Answer is:
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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