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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). The 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
The lines are drawn from origin O with d.cs proportional to (1,1,1),(2,3,0) and (1,0,3)
Consider, ∣ ∣111230103∣ ∣
=1(90)+1(60)+1(0+3)
=9+9=0
Δ=0
Hence, the lines are co-planar.

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