Compute the cross product of two 3D vectors, plus the dot product, magnitudes and the angle between them.
How cross product is worked out
The cross product produces a vector perpendicular to both inputs, with a magnitude equal to the area of the parallelogram they span. It is the operation behind torque, angular momentum and surface normals in graphics.
The dot product is shown alongside because the two together characterise the relationship completely: the dot product measures how parallel the vectors are, the cross product how perpendicular.
How to fill it in
- Enter the three components of vector a.
- Enter the three components of vector b.
- Read the cross product, dot product and angle.
The maths behind it
A worked example
Take the starting scenario, a vector a of 3, vector b of 4. That gives a cross product a × b of (-15, -2, 39). Underneath, Dot product comes out at -13 and Angle between at 107.263°. Change any field and every figure updates as you type.