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Question

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

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

The correct option is C exactly two values
∣ ∣21344511kk21∣ ∣=0

∣ ∣11111kk21∣ ∣=0
1(1+2k)+1(1+k2)1(2k)=0
k2+3k=0
k=0, k=3
Hence, k has exactly two values.

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