Mathematics & Statistics • Analytic Geometry & Vectors
Vector Operations
5 min read
The dot product answers "how much of one vector lies along the other" and gives angles and projections. The cross product gives a vector perpendicular to both, which is exactly a moment: M = r × F.
Worked: angle and normal
| Step | Result |
|---|---|
| A = (2, −1, 3), B = (1, 4, 2) | |
| A·B = 2 − 4 + 6 | 4 |
| |A| = √14, |B| = √21 | 3.742, 4.583 |
| cos θ = 4 / (3.742 × 4.583) | 0.233, so θ ≈ 76.5° |
| A × B | (−14, −1, 9) |
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