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Vectors formulas
16 formulas for Vectors, from the Vectors, Probability & Statistics section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Magnitude | |a| = √(a₁² + a₂² + a₃²) | |
| Unit vector | â = a / |a| | |
| Dot product | a·b = |a||b| cos θ = a₁b₁ + a₂b₂ + a₃b₃ | |
| Angle between vectors | cos θ = a·b / (|a||b|) | |
| Perpendicular | a·b = 0 | |
| Projection of a on b | (a·b) / |b| | |
| Cross product | a × b = |a||b| sin θ n̂ | |
| Cross product (components) | |i j k; a₁ a₂ a₃; b₁ b₂ b₃| | |
| Parallel | a × b = 0 | |
| Area of parallelogram | |a × b| | |
| Area of triangle | ½ |a × b| | |
| Scalar triple product | [a b c] = a·(b × c) | volume of parallelepiped |
| Coplanar | [a b c] = 0 | |
| Vector triple product | a × (b × c) = (a·c)b − (a·b)c | |
| Section formula | r = (m b + n a)/(m + n) | |
| Unit vectors | i·i = 1, i·j = 0; i × j = k, j × k = i, k × i = j |
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