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Find the equation of the plane that contains the point (3, 2, 0) and also includes the line given by (x-4)/1 = (y-7)/5 = (z-4)/4.

1. x - y + z = 1
2. x + y + z = 5
3. x + 2y - z = 1
4. 2x - y + z = 5

Correct answer: x - y + z = 1

Solution

The equation of the plane must satisfy the point (3, 2, 0) and be parallel to the direction vector of the given line. The correct option, x - y + z = 1, can be verified by substituting the point into the equation, confirming it lies on the plane.

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