The Cross Product: Orthogonality Proof + The Right Hand Rule

Math Easy Solutions

description

In this video I go over the orthogonality or perpendicular theorem for cross products and prove that it is indeed true. The cross product of two non-zero vectors produces a vector that is orthogonal or perpendicular to the two vectors. I prove this by showing that the dot product of the cross product with either vector that produces it is equal to 0, hence they are perpendicular as per my earlier video on the Dot Product.

Also in this video I go over the Right-Hand Rule convention for the cross product. This rule is such that the cross product produces a vector in the direction of your right-hand thumb while your fingers curl in the direction from the starting vector a to the ending vector b.

The timestamps of key parts of the video are listed below:

Cross Product Orthogonality Proof: 0:00
Right Hand Rule: 6:01

This video was taken from my earlier video listed below:

Vectors and the Geometry of Space: The Cross Product: https://youtu.be/k8GRt95i-Gc
Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FuRJ8rg-YVQvfPoPOwhuRW