Line positions and traces

Line r passes through A(13, 5, 3) with direction (0, 6, 8). Classify it and find its traces.

Step-by-step solution

Look at the direction components: a zero component tells you which plane the line is parallel to.
Draw H where the line cuts the PH (z = 0). If the direction has z = 0, the line is parallel to the PH and has no horizontal trace.
Draw V where it cuts the PV (y = 0). If the direction has y = 0, it is parallel to the PV and has no vertical trace.
Check: H(13, 2.75, 0); V(13, 0, -3.67).

Result: profile line. H(13, 2.75, 0); V(13, 0, -3.67).

A line parallel to a plane has no trace with that plane: it is not a mistake, it simply does not cut it.