Definition of Orthogonal Vectors

This video provides a definition of orthogonal vectors. Two vectors in Rn are orthogonal if their dot product is zero. We provide a graphical depiction of orthogonality and why the dot product must be zero using our previous definitions of distance. We also work a few examples where we determine if two provided vectors are orthogonal (or not) by computing their dot product.

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[autumnfox]

Thank you for making these videos! Bought access to the other videos too!

[tubesteaknyouri]

Thank you for your videos. I find them to be very helpful.

As I was watching this video, I wondered if this might form a basis for a geometric interpretation of the variance sum law from statistics. The definition of distance looks similar to the variance sum law, which states Var[X + Y] = Var[X] + Var[Y] + 2 Covar[X, Y]. Or perhaps the apparent similarity is merely superficial.