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The plane through the intersection of the planes x + y + z = 1 and 2x + 3y − z + 4 = 0 and parallel to y-axis also passes through the point:

1. (−3, 0, −1)
2. (−3, 1, 1)
3. (3, 3, −1)
4. (3, 2, 1)

Correct answer: (3, 2, 1)

Solution

The family (1+2L)x+(1+3L)y+(1-L)z+(4L-1)=0 is parallel to the y-axis when 1+3L=0, i.e. L=-1/3, giving x+4z-7=0. The point (3,2,1) satisfies 3+4-7=0.

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