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Two vectors are oriented at 90° to each other. What is their dot product?


If u and v are orthogonal, then u · v   =   |u| |v| cos 90°   =   |u| |v| 0.0   =   0.0

Dot Product of Orthogonal Vectors

This fact is of fundamental importance. It works for vectors of all dimensions:

The dot product of orthogonal vectors is zero.

"Orthogonal" means "oriented at 90° to each other". To keep things consistent, the zero vector is regarded as orthogonal to all other vectors since 0 · v = 0.0 for all vectors v .


Say that two vectors s and t have a dot product that is zero.