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Question

The lines x−21=y−31=z−4−k and x−1k=y−42=z−51 are coplanar if-


A
k=1 or 1
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B
k=0 or 3
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C
k=3 or 3
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D
k=0 or 1
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Solution

The correct option is B k=0 or 3
For two lines to be coplaner,
∣ ∣x2x1y2y1z2z1a1b1c1a2b2c2∣ ∣=0
∣ ∣11111kk21∣ ∣=01(1+2k)1(1+k2)+1(2k)=0
k2+3k=0k=0,3
Hence, option 'B' is correct.

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