Vector Calculator
Enter two vectors with 2 or 3 components each. This calculator finds the magnitude of each, their dot product, their cross product and the angle between them, with each formula shown.
Frequently asked questions
What is the dot product?
The dot product multiplies matching components and sums them; it is zero exactly when the vectors are perpendicular.
What does the cross product give?
For 3D vectors it gives a vector perpendicular to both; for 2D vectors the result is reported as a single scalar.
How is the angle between vectors found?
From the dot product: the cosine of the angle equals a·b divided by the product of the magnitudes.