The Cross Product | Calculus 3 Lesson 12 - JK Math
How to Find The Cross Product of Vectors (Calculus 3 Lesson 12)
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In this video you will learn how to find the cross product of two vectors. The cross product, like the dot product, is a way to multiply two vectors together. However, unlike the dot product, which produces a scalar, the cross product produces another vector. In particular, the vector that results will be a vector that is orthogonal/perpendicular to both vectors involved in the cross product. We discuss how to find the cross product by using determinants, how to use the right hand rule to determine a cross product’s direction, an alternate way to find a cross product, and the properties of the cross product. Additionally, we practicing find the cross product of two vectors 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 is the Cross Product? / Review of Determinants
5:23 Finding a Cross Product Using Determinants
14:14 Important Notes About the Cross Product
18:46 Example: Finding a Cross Product
27:17 Finding an Alternate Form of the Cross Product
40:57 Cross Product is Zero?
44:11 Summary of Formulas
45:16 Properties of the Cross Product
📝 Examples Video: • Cross Product Examples | Calculus 3 - JK Math
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Corrections:
31:00 Note that the work here is correct, but I did make a typo. The first term of the third quantity in the first line should be v1²u2², not v1²u1². That same correction should be made to the red underlined term in the second and third lines of the work. After that, the term disappears via factoring, and that factoring is correct as it is based on the work without the typo.
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