Vector Addition Calculator: Determine Resultant Using Law of Cosines

Calculate Resultant Vector Magnitude and Direction

Enter the angle θ between Vector 1 and Vector 2 (0-180°).

Use our Vector Addition Calculator to find the resultant vector's magnitude and direction quickly and accurately. This tool applies the Law of Cosines, simplifying complex physics and engineering problems. Input two vector magnitudes and the angle between them to get your answer instantly.

Formula:

Resultant Magnitude (R): R = √(V₁² + V₂² + 2VV₂ cos(θ))

Direction (α): α = arcsin(((V₂ × sin(θ)) / R))

Where:

  • R: Magnitude of the resultant vector
  • V: Magnitude of Vector 1
  • V: Magnitude of Vector 2
  • θ: Angle between Vector 1 and Vector 2 (in degrees, tail-to-tail)
  • α: Angle of the resultant vector relative to Vector 1 (in degrees)

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