If the point (3, 1, 7) is reflected across the plane x − y + z = 3, and the resulting image point is P, what is the equation of the plane that passes through P and includes the line given by x/1 = y/2 = z/1?

x + y − 3z = 0
3x + z = 0
x − 4y + 7z = 0
2x − y = 0

Correct answer: x − 4y + 7z = 0

Solution

The reflection of the point (3, 1, 7) across the plane x − y + z = 3 gives the image point P. The plane passing through P and containing the given line is determined to have the equation x − 4y + 7z = 0.

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