The Dot Product

The dot product of two vectorsandis a number. It is the length of the of vector projected onto the unit vector in the direction ofIfis the angle betweenand then from the diagram aboveThis equation is usually writtenorand this form can be used to find the angle between two vectors.

To find the dot product of two vectors written in component form we multiply corresponding coordinates and add all the answers.

Example: Find the dot product ofand

Written in vector ijk notation this would be

and

The angle between the two vectors is the solution to

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