Vector Calculator
Add, Subtract, Dot, Cross & Magnitude.
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Vector Properties
Magnitude |A|
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Unit: -
Magnitude |B|
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Unit: -
Operations
- A + B Addition -
- A − B Subtraction -
- A · B Dot Product -
- A × B Cross Product -
- Angle (θ) -
2D Projection (X-Y Plane)
What are Vectors?
[Image of vector components diagram]A Vector is a quantity that has both magnitude (size) and direction. Examples include Force, Velocity, and Displacement. In contrast, a Scalar only has magnitude (like Temperature or Mass).
Formulas Used
- Magnitude:
|A| = √(x² + y² + z²) - Dot Product (Scalar):
A · B = (Ax × Bx) + (Ay × By) + (Az × Bz). Used to find the angle between vectors or work done. - Cross Product (Vector): Result is a new vector perpendicular to both A and B. Used to find Torque or Magnetic Force.
- Angle (θ):
θ = cos⁻¹[ (A · B) / (|A| × |B|) ]