In the cross product of two vectors the resulting vector seems to sometimes have a component in a direction perpendicular to the plane of the first two vectors. This seems to create something out of nothing - is this right or have I misunderstood?

Question

In the cross product of two vectors the resulting vector seems to sometimes have a component in a direction perpendicular to the plane of the first two vectors.  This seems to create something out of nothing - is this right or have I misunderstood?

waynex · Answer

Ah, the cross product is always perp to the two original vectors. This is a very important concept in vector math. It does seem like something out of nothing, but the cross product calculation was in fact designed to do exactly this very thing. If you take 18.02, multivariable calculus, you will learn all about the cross product. Cheers for noticing this property of it!