Question 16 (2 points)
Determine the symmetric equation of the line that is parallel to the line going through the points $P(1,5,-2)$ and $Q(-2,6,2)$ which passes through the origin.

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Answer

Write the symmetric equation of the line parallel to PQ and passing through the origin: $\boxed{\frac{x}{-3} = \frac{y}{1} = \frac{z}{4}}$

Steps

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: $\boxed{\frac{x}{-3} = \frac{y}{1} = \frac{z}{4}}$