Dot Product and Projection

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
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