![]() ![]() The goal is to apply one vector to another. You've seen the dot product equation everywhere:Īnd also the justification: "Well Billy, the Law of Cosines (you remember that, don't you?) says the following calculations are the same, so they are." Not good enough - it doesn't click! Beyond the computation, what does it mean? Vector fields are an important tool for describing many physical concepts, such as gravitation and electromagnetism, which affect the behavior of objects over a large region of a plane or of space. With the quaternions (4d complex numbers), the cross product performs the work of rotating one vector around another (another article in the works!). In particular, vector fields can be used to develop several higher-dimensional versions of the Fundamental Theorem of Calculus.“Multiply” two vectors when only perpendicular cross-terms make a contribution (such as finding torque).Determine if two vectors are orthogonal (checking for a dot product of 0 is likely faster though).Find the signed area spanned by two vectors.Find the direction perpendicular to two given vectors.(Try it: using your right hand, you can see x cross y should point out of the screen). In a computer game, x goes horizontal, y goes vertical, and z goes “into the screen”. The Unity game engine is left-handed, OpenGL (and most math/physics tools) are right-handed. ![]() I never really memorized these rules, I have to think through the interactions. This completed grid is the outer product, which can be separated into the:ĭot product, the interactions between similar dimensions ( x*x, y*y, z*z)Ĭross product, the interactions between different dimensions ( x*y, y*z, z*x, etc.) Taking two vectors, we can write every combination of components in a grid:
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