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Question

The equation of the plane containing the two lines of intersection of the two pairs of planes x + 2y – z – 3 = 0 and 3x – y + 2z – 1 = 0, 2x – 2y + 3z = 0 and x – y + z + 1 =0 is :

A
7x – 7y + 8z + 3 = 0
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B
7x – 8y + 9z + 3 = 0
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C
5x – 5y + 6z + 2 = 0
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D
None of these
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Solution

The correct option is D None of these
The planes through given lines of intersection are
(x+2yz3)+λ(3xy+2z1)=0....(1)
and (2x2y+3z)+μ(xy+z+1)=0....(2)
Planes (1) and (2) are same. Comparing the coefficients,
we get, 1+3λ2+μ=2λ2μ=1+2λ3+μ=3λμ
Solving for λ,μ, these equations are inconsistent. Therefore, there exists no such plane i.e., the lines are neither parallel nor intersecting.

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