5.5 Dot Product

OpenStax Precalculus 2e — Chapter 8, Section 8.8 (dot product) + supplementary

Learning Objectives

  • Compute the dot product: \(\mathbf{u} \cdot \mathbf{v} = u_1v_1 + u_2v_2\)

  • Find the angle between vectors: \(\cos\theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}\)

  • Determine orthogonality (\(\mathbf{u} \cdot \mathbf{v} = 0\))

  • Compute the projection of one vector onto another

Key Concepts

To be filled during study.

Practice Problems

To be completed with textbook exercises.

Section Summary

To be written after completing the section.

Study Notes

Personal observations and connections to engineering work.