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Calculus II Project Title
Dot Products
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 <u1,u2> and <v1,v2> (in two dimensions) or <u1,u2,u3> and <v1,v2,v3> (in three dimensions).
It is defined to equal:
u v = u1v1 + u2v2
u v = u1v1 + u2v2 +u3v3

What's special about a dot product?
A dot product has five properties that can be useful in different situations.
  1. u v = v u (Known as the commutative property)
  2. u (v + w) = u v + u w (Known as the distributive property)
  3. c(u v) = cu v = u cv
  4. 0 v = 0
  5. v v = ||v||²
Note: These properties assume c to be a scalar.
Where to from here?
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