Vector Calculations

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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.

Vector Calculations

Operation

Addition Subtraction Dot Product Vector Product Magnitude Unit Vector Angle

Vector A

Vector B

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