Vector Projections & Orthogonal Components | Calculus 3 Lesson 10 - JK Math
How to Find Vector Projections & Orthogonal Components (Calculus 3 Lesson 10)
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In this video you will learn how to find the vector components of a vector in relation to another vector. In particular, you will learn how to find a vector component of a vector parallel to another vector (vector projection) and a vector component of a vector perpendicular/orthogonal to another vector. You will learn the formulas for finding these vectors, including where they come from, and then how to use them with an example problem.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 What are Vector Components?
2:22 Parallel & Orthogonal Vector Components
11:06 Finding the Projection Vector Formula
21:18 Summary of Formulas
24:12 Example: Finding Projections & Orthogonal Components
Corrections:
32:39 I made a sign error here. When subtracting, -8/21 becomes positive resulting in a j term of 50/21, not 34/21.
📝 Examples Video: • Vector Projections & Orthogonal Components...
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