The Dot Product of Vectors - Concept

Concept Concept (1)

An operation used frequently on vectors is the vector dot product, sometimes known as the scalar product. The vector dot product is an operation on vectors that takes two vectors and produces a scalar, or a number. The vector dot product can be used to find the angle between two vectors, and to determine perpendicularity. It is also used in other applications of vectors such as with the equations of planes.

Sample Sample Problems (3)

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The Dot Product of Vectors - Problem 1
Problem 1
How to compute the dot product of two vectors, and how to demonstrate that the dot product is commutative.
The Dot Product of Vectors - Problem 2
Problem 2
How to compute the dot product of two vectors, and how to demonstrate that the dot product distributes over addition.
The Dot Product of Vectors - Problem 3
Problem 3
How to prove that the dot product uu of a vector with itself equals the square of its magnitude abs(u)^2.