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A plane p contains the line L1: y/b + z/c = 1, x = 0 and is parallel to the line L2: x/a - z/c = 1, y = 0. With a = b = c = 1, find the distance from the image of the point A(a, 0, 0) in the plane p to the point M(-5/3, 8/3, 11/3).

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

With a=b=c=1, the plane p containing L1 and parallel to L2 has equation x - y - z + 1 = 0. The reflection of A(1,0,0) in this plane is A'(-1/3, 4/3, 4/3). The distance from A' to M(-5/3, 8/3, 11/3) is sqrt(16/9 + 16/9 + 49/9) = sqrt(81/9) = 3.

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