Lesson: Cross Product in 3D Mathematics

In this lesson, we will learn how to find the cross product of two vectors in space and how to use it to find the area of geometric shapes.

Lesson Plan

Students will be able to

define the cross product of two vectors as the product of the magnitudes multiplied by the sine of the angle between the vectors,
calculate the cross product of two vectors in space using their components (i.e., a determinant),
understand the properties of the cross product in 3D,
use the geometric meaning of cross product to solve problems, in particular, finding lengths or areas.

Q1:

Find .

Q2:

Given that and , find .

Q3:

Let and . Calculate .