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Line parallel to another through a point

Through P(17, 6, 12) draw line s parallel to r, which passes through A(10, 2, 6) with direction (6, 6, 3).

Step-by-step solution

1. Two lines are parallel if they have the same (or proportional) direction.
2. Keep the direction of r and place point P.
3. If P lies on r, the line coincides with r: it is not a different parallel.
4. Check that the matching projections are parallel.

Result: s passes through P(17, 6, 12) with the direction of r.

Through a point outside a line only one parallel passes; through a point on the line, the parallel is the line itself.

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