Vectors
Adding up the arrows…
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Vectors
Adding up the arrows…
Two vectors in 3D make a third that stands perpendicular to both, as long as the parallelogram they span is large, pointing where your right thumb points. Orbit it and see.
In 3D there is a product of two vectors that gives another vector. Start simple: a = (2, 0, 0) along x and b = (0, 2, 0) along y. They span a 2 × 2 square, shaded yellow.
The cross product appears once the tour reaches it.
Each component of a × b leaves out one axis: the x-component uses only y and z, and so on round the cycle x → y → z → x. That cycle is where the right-hand rule comes from.