Vectors in the plane
Problem 9.272 · easy
Find \( \displaystyle \overrightarrow{PQ} \) in component form and its length, for \( \displaystyle P(5, 2) \) and \( \displaystyle Q(-3, 6) \).
- \[ \left[\begin{matrix}-8\\4\end{matrix}\right] \]Terminal point minus initial point.✓ Proved
- \[ 4 \sqrt{5} \]√(x² + y²).✓ Proved
Answer \( \left\langle -8, 4 \right\rangle,\ \|\overrightarrow{PQ}\| = 4 \sqrt{5} \)
✓ Nihil obstat Every line of this solution was proved by the computer algebra system SymPy. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation.
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | ✓ Proved | sympy 1.14.0 | simplify(lhs - rhs) reduced to 0 |
| 2 | ✓ Proved | sympy 1.14.0 | simplify(lhs - rhs) reduced to 0 |
| answer, a second way | ✓ Checked independently | sympy 1.14.0 + mpmath 1.3.0 | floating point |
Reviewers
gpt-oss:20b: passqwen3.6:27b-mlx: pass — The solution correctly computes the vector components and magnitude, and the annotations accurately describe the methods used.
Every verdict on record (4)
qwen3.6:27b-mlx: pass 2026-10-05 — The solution correctly computes the vector components and magnitude, and the annotations accurately describe the methods used.gpt-oss:20b: pass 2026-10-05qwen3.6:27b-mlx: pass 2026-10-05 — The solution correctly computes the vector components and magnitude. The comments accurately describe the methods used.gpt-oss:20b: pass 2026-10-05
Proved: SymPy reduced the difference between the two sides to zero. Checked independently: a separate
method, named above, confirmed it. Checked numerically: the two sides agree at every sampled point, which is evidence,
not proof. Reviewed: a model or a person read it; that is all a sentence can have. Solution by
generator:structured/vectors_plane, checked 2026-10-05 with SymPy 1.14.0.