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Line parallel to a plane through a point

Statement. Through point P(2, 6, 6), draw a horizontal line parallel to plane P: x + y + z = 6.

Step-by-step solution

1. A line is parallel to a plane if its direction is perpendicular to the normal of the plane.
2. For it to be horizontal as well, its direction must have z = 0.
3. With those two conditions, the direction is d = n x (0, 0, 1) = (1, -1, 0).
4. Draw the line through P with that direction. Both projections are parallel to the ground line.

Result

r passes through P(2, 6, 6) with direction (1, -1, 0).

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