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Question

The equation of the plane containing the lines

r=a1+λa2 and r=a2+μa1 is


A

[r a1 a2]=0

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B

[r a1 a2]=a1.a2

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C

[r a1 a2]=|a1||a2|

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D

None of these

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Solution

The correct option is A

[r a1 a2]=0


The required plane passes through a point having position vector a1 and is parallel to the vectors a1 and a2. If r is the position vector of any point on the plane, then (ra1), a1, a2 are coplanar.
Therefore (ra1).(a1×a2)=0[r a1 a2]=[a1 a1 a2][r a1 a2]=0 ( [a1 a1 a2]=0)
Hence, the required plane is [r a1 a2]=0


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