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Question

If for some αR, the lines L1:x+12=y21=z11 and L2:x+2α=y+15α=z+11 coplanar, then the line L2 passes through the point:

A
(2,10,2)
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B
(10,2,2)
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C
(10,2,2)
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D
(2,10,2)
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Solution

The correct option is A (2,10,2)
A(1,2,1),B(2,1,1)
[AB b1 b2]=0
∣ ∣132211α5α1∣ ∣=0
1(1+α5)+3(2α)2(102α+α)=0
6α+63α+2α20=0
82α=0
α=4
Checking Point satisfies L2
L2:x+24=y+19=z+11
Any point on L2 is (4k2,9k1,k1)

From given options, for point (2,10,2):
44=99=11
Therefore, option (a) is correct.

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