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Question

Three lines are drawn from the origin O with direction cosines proportional to (1,1,1), (2,3,0) and (1,0,3), Then three lines are

A
not coplanar
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B
coplanar
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C
perpendicular to each other
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D
coincident
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Solution

The correct option is B coplanar
Let Δ=∣ ∣111230103∣ ∣
If line are perpendicular to each other then Δ0
or If line are coplaner then Δ=0
Δ=∣ ∣111230103∣ ∣

C2C2+C1C3C3C1
∣ ∣100212112∣ ∣=1(2+2)=0
Hence three lines are coplanar

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