Math Is Fun Forum

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Cross Product understanding for newbie

Anyone here understand how a cross product works in relation to 3D ? I understand the core of what it does which is the third vector from the other two vectors but relating that to 3D space has been the issue.  Here is my theory of how it works, suppose you have a sphere and a plane in a scene, the sphere is traveling on the Y axis, that is one vector, the plane is static, which is another vector, the X axis.  When the sphere touches or hits the plane, the cross product would be the axis or vector to the right of the sphere and plane, suppose that is behind the sphere, when the sphere touches the plane, it will create a red mark which is the cross product of the sphere and the plane ?

Is my theory somewhat correct, or completely wrong ?

zetafunc

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Registered: 2014-05-21

Posts: 2,436

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Re: Cross Product understanding for newbie

Well, your geometric picture is correct, although I'm not sure what you mean by a red mark (the direction of that mark needs to be perpendicular to the sphere's direction of motion and the plane, including with the right orientation). You can use the right-hand rule and rotate your hand around.

Maths Is Fun has a webpage about this here.

Michael Spivak's Calculus on Manifolds gives a more sophisticated viewpoint of the cross product, but is consistent with its usual definition, and shows how the cross product fits in with the other concepts discussed in that text (in this case, an alternating 1-tensor). But I don't recommend going through that chapter without a first course in linear algebra. The Wikipedia page on the subject has some nice discussions.

Last edited by zetafunc (2016-10-03 08:58:45)