Step 1 :Find the direction vector of the line going through points P(1,5,-2) and Q(-2,6,2): \(\vec{d} = Q - P = \langle -3, 1, 4 \rangle\)
Step 2 :Write the symmetric equation of the line parallel to PQ and passing through the origin: \(\boxed{\frac{x}{-3} = \frac{y}{1} = \frac{z}{4}}\)