Vector Projection Calculator

Summary

Enter two 2D or 3D vectors and instantly get the scalar projection, vector projection, and full step-by-step working.

How it works

1. Choose 2D or 3D mode and enter the components of vector A and vector B.
2. The tool computes the dot product A · B.
3. It then finds the magnitude of B: |B| = sqrt(Bx² + By² [+ Bz²]).
4. The scalar projection is computed as: comp = (A · B) / |B|.
5. The unit vector of B is found: B̂ = B / |B|.
6. The vector projection is computed as: proj = (A · B / |B|²) × B, shown component by component.

Use cases

• Find how much of one vector lies in the direction of another in physics problems.
• Compute the component of force along an inclined plane.
• Solve linear algebra homework requiring orthogonal decomposition.
• Verify manual projection calculations step by step.
• Calculate shadow length (projection) of one vector onto an axis.
• Decompose velocity into parallel and perpendicular components.

Frequently Asked Questions