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Question

If the lines x21=y31=z4k and x1k=y42=z51 are coplanar, then k can have

A
exactly one value
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B
exactly two values
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C
exactly three values
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D
any value
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Solution

The correct option is B exactly two values
We have, ∣ ∣11111kk21∣ ∣=0
1(1+2k)+1(1+k2)1(2k)=0

k2+1+2k+12+k=0

k2+3k=0

(k)(k+3)=0

Thus k has 2 values.

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