Cross product
Cross product is an interactive experiment in Vectors, a free simulation from StudyFi Lab that runs right in your browser.
The cross product a × b is a vector perpendicular to both a and b. The right-hand rule gives its direction, and its length |a × b| = |a|·|b|·sin φ equals the area of the parallelogram spanned by a and b. It is zero for parallel vectors, and swapping the factors flips it: b × a = −(a × b).
Try this: Set a = (3, 0, 0) and b = (0, 2, 0): a × b points along the z axis with length 6, just like the 3 × 2 rectangle. Then tilt b towards a and watch the area shrink.
Frequently asked questions
What does the “Cross product” experiment show?
The cross product a × b is a vector perpendicular to both a and b. The right-hand rule gives its direction, and its length |a × b| = |a|·|b|·sin φ equals the area of the parallelogram spanned by a and b. It is zero for parallel vectors, and swapping the factors flips it: b × a = −(a × b).
How do I try “Cross product”?
Set a = (3, 0, 0) and b = (0, 2, 0): a × b points along the z axis with length 6, just like the 3 × 2 rectangle. Then tilt b towards a and watch the area shrink.
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