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This page will help you understand the concept of a dot product and how to calculate one. What is a dot product? The dot product is an operation between two vectors that returns a scalar quantity. This is significant because most other vector operations return another vector. Formally, the dot product takes two input vectors u and v defined as <u_{1},u_{2}> and <v_{1},v_{2}> (in two dimensions) or <u_{1},u_{2},u_{3}> and <v_{1},v_{2},v_{3}> (in three dimensions). It is defined to equal: u v = u_{1}v_{1} + u_{2}v_{2} +u_{3}v_{3} What's special about a dot product? A dot product has five properties that can be useful in different situations.
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