## Dot Product and Projection

In this section we will learn about the **dot product **of two vectors which is quite useful in higher-dimensional geometry, physics, statistics, etc. For example, dot product makes it very easy to find the shortest distance between a line and a point not on the line.

**Learning Objectives:**

- Definition of dot product
- Properties of dot product
- Geometric Interpretation of Dot Product
- Orthogonality
- Projection of a vector onto another vector
- Component of projection
- Decomposing a given vector as the sum of two orthogonal vectors
- Applications of Dot Product
- shortest distance between a point and a line.
- Force and work done
- Cauchy-Schwartz Inequality