Introduction

Vector Projection

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:

Vector Projection

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

Vector Projection

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

Vector Projection

Since a1 is in the same direction as b,

Vector Projection

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

Vector Projection

References & Resources

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