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Question

If the lines x12=y+13=z14 and x31=yk2=z1 intersect, then k is equal to

A
1
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B
29
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C
92
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D
0
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Solution

The correct option is C 92
Here we can take four vectors

For line x12=y+13=z14:
a=^ij+k
b=2i+3j+4k

For line x31=yk2=z1:
c=3i+kj
d=i+2j+k
If these lines intersect, then (ac),b and d should be coplanar

[(ac),b,d]=0

∣ ∣2k+11234121∣ ∣=0

2(5)(k+1)(2)+(1)(1)=0
(k+1)(2)=11
k=92

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