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Question: Answered & Verified by Expert
If the lines r=i^-j^+k^+λ3j^-k^ and r=αi^-j^+μ2i^-3k^ are co-planar, the the distance of the plane containing these two lines from the point α,0,0 is
MathematicsThree Dimensional GeometryJEE MainJEE Main 2022 (26 Jun Shift 2)
Options:
  • A 29
  • B 211
  • C 411
  • D 2
Solution:
2132 Upvotes Verified Answer
The correct answer is: 211

Given,

r=i^-j^+k^+λ3j^-k^      ...L1

r=αi^-j^+μ2i^-3k^

 L1 and L2 are coplanar then a2-a1b1b2=0

So, 03-120-31-α01=0

-32+31-α=0

3α=5

α=53
Now, normal vector will be, n=i^j^k^03-120-3=i^-9-j^2+k-6

=9,2,6

So, equation of plane is given by, 

9x-1+2y+1+6z-1=0

9x+2y+6z-13=0

Now finding perpendicular distance from α,0,0

=9·53+0+0-1381+36+4=2121=211

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