Vector Operations:
- Addition: a⃗ + b⃗ = (a₁+b₁, a₂+b₂, a₃+b₃)
- Subtraction: a⃗ - b⃗ = (a₁-b₁, a₂-b₂, a₃-b₃)
- Dot Product: a⃗·b⃗ = a₁b₁ + a₂b₂ + a₃b₃
- Cross Product: a⃗×b⃗ = (a₂b₃-a₃b₂, a₃b₁-a₁b₃, a₁b₂-a₂b₁)
- Magnitude: |a⃗| = √(a₁² + a₂² + a₃²)
- Unit Vector: â = a⃗/|a⃗|
- Angle: cos θ = (a⃗·b⃗)/(|a⃗|·|b⃗|)
Note: Separate vector components by commas.