Home › Collection › Parallelism and perpendicularity › Plane parallel to a line

Plane parallel to a line

Find a plane α through P(17, 11, 7) parallel to line r, which passes through A(16, 10, 4) with direction (3, 1, 3).

Step-by-step solution

1. A plane is parallel to a line if the line direction is perpendicular to the plane normal.
2. Choose a normal perpendicular to the direction and through P.
3. Check that r is not contained in α: if it were, it would be another case.

Result: α has normal (-6, 6, 4) through P(17, 11, 7).

A single line does not determine a plane: that is why infinitely many planes parallel to r pass through P.

PractiseBack to the block