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**Vector Basics - Sketch**

What is a vector? What are its parts? When are two vectors equal?**Vectors and Points 1 -****Sketch or Picture**

How do you assign a pair of coordinates to a vector?**Vectors and Points 2 -****Sketch or Picture**

Suppose a vector isn't sitting with its tail at the origin? What are its coordinates?**Vector Addition: Geometry -****Sketch or Picture**

What's the geometric definition of the sum of two vectors?**Vector Addition: Algebra -****Sketch or Picture**

How do you add vectors in terms of components?**Vector Subtraction -****Sketch or Picture**

What's the difference between two vectors?**Length -****Sketch or Picture**

What's the length of a vector?**Unit Vectors -****Sketch or Picture**

What's a unit vector?**Unit Vectors and Unit Circle -****Sketch or Picture**

How do unit vectors relate to the unit circle? What are the components of a unit vector in terms of the circular functions?**Unit Vectors from Others -****Sketch or Picture**

Given a nonzero non-unit vector, what's a unit vector pointing in the same direction?**Definition of the Dot Product -****Sketch or Picture**

What is the dot product of two vectors? How does it relate to length?**Dot Product of Unit Vectors -****Sketch or Picture**

What's the dot product of two unit vectors?**Dot Products of Non-Unit Vectors -****Sketch or Picture**

What's the dot product of non-unit vectors?**Why dot products?**

What are dot products good for?**Projection: Theory -****Sketch or Picture**

What's the projection of one vector on another?**Projection: Numbers -****Sketch or Picture**

For those who find numbers comforting.**Decomposition of Vectors -****Sketch or Picture**

How can you write a vector as a sum of a vector parallel to a given vector and a vector perpendicular to the vector?**The Cross Product -****Sketch or Picture**

What is the cross product of two vectors?

A history of the vector concept (which goes well beyond what we've touched on here) can be found in the MacTutor History of Mathematics archive.