this question is a repost from math stackexchange because that guy worded the question so perfectly the question i really wanted to ask about cross products. *please see image below*(adsbygoogle = window.adsbygoogle || []).push({});

as far i can understand, the formula for the cross product is basically that the idea of a cross product is sort of symmetrical to the idea of taking the determinant of a 3x3 matrix(or volume of a parallelepiped) which involves a vector orthogonal to the plane formed by two vectors. and by setting i=<1,0,0>, j=<0,1,0> and, k=<0,0,1>... we in turn get iC_11 + jC_12 + kC_13 such that C_ij are cofactors. thus, the reason why when we take the magnitude of the orthogonal vector, we get the same numeric value of the area of the parallelogram.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Motivation and proof behind cross products

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**