Question

The pdf on Cross Product says: "Example: It is possible to compute a cross product using the algebraic facts and the known products of i, j and k. For example,
(2i + 3j) × (3i − 2j) = (6i × i) − (4i × j) + (9j × i) − (6j × j) = −13k.
The first equation follows from the distributive law.

Can someone explain how you get (6i × i) − (4i × j) + (9j × i) from the initial equation? The distributive law makes it seem like we should use normal algebra and it should be 6i^2 - 4ij + 9ij - 6j^2

Answer 1

2i x 2j isn't 4ij. It's 4( i x j ), i.e 4 times the cross product of the i and j vectors.

And remember that the cross product is not commutative. i x j= k but j x i = -k