Vector Operations Calculator
Vector operations calculators handle 2D and 3D vector mathematics: addition, subtraction, scalar multiplication, dot product, cross product, and magnitude.
- 1Addition: a + b = (a₁+b₁, a₂+b₂, a₃+b₃)
- 2Dot product: a·b = a₁b₁+a₂b₂+a₃b₃ (scalar)
- 3Cross product: a×b = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)
- 4Magnitude: |a| = √(a₁²+a₂²+a₃²)
a=(3,1,−2) and b=(1,4,2)=Dot product = 3+4−4 = 3; |a| = √14 ≈ 3.74
| Operation | Formula | Result |
|---|---|---|
| Addition | (a₁+b₁, a₂+b₂, a₃+b₃) | Vector |
| Subtraction | (a₁−b₁, a₂−b₂, a₃−b₃) | Vector |
| Dot product | Σaᵢbᵢ | Scalar |
| Cross product | Determinant formula | Vector (3D only) |
| Magnitude | √(Σaᵢ²) | Scalar |
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