## Vector Projection

### Introduction

If **a** and **b** are two vectors, the vector projection of **a** on **b** is the vector **a1** with the same direction as **b** and with the length:

When θ is not known, we can compute cosθ using the following property of Dot Product a∙b:

Thus, the length of a1 can be also computed as follows:

Since a1 is in the same direction as b,

Where is the Unit Vector with the same direction as b:

### References & Resources

- Wikipedia - http://en.wikipedia.org/wiki/Vector_projection

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