Watch on YouTube - Video notes - Video sections playlist - Vectors and the Geometry of Space playlist
In this video I go over a review of the cross product, its definition and formulas, as well its many useful applications in mathematics and physics. The definition of the cross product involves cross-multiplication, subtraction, and addition, which can be simplified using determinates. The cross product is defined as such because it has many useful properties, namely that it gives a perpendicular vector normal to the two vectors it comprises. This property makes it ideal for dealing with angular momentum and torque. The cross product can also be used to obtain the area of a parallelogram and the volume of the parallelepiped. The volume formula involves the dot product and cross product in what is known as the scalar triple product. The cross product has many other applications in physics, geometry, and computer graphics.
Timestamps:
Question 8: Cross product formula: 0:00
Solution: Cross product angle formula: 0:17
Definition of cross product: 1:57
Determinant form of the cross product: 3:13
Question 9: Properties of cross product: 6:28
(1) Determining perpendicular vector: 6:39
(2) Calculating area of a parallelogram: 6:54
(3) Calculating volume of a parallelepiped: 7:52
(4) Calculating Torque: 10:06
The Cross Product and its Useful Properties