This small group activity is designed to help students visualize the cross product.
Students work in small groups to determine the area of a triangle in space.
The whole class wrap-up discussion emphasizes the geometric interpretation of the cross product.
What students learn
Encourages students to master both the algebraic and geometric expressions for the cross product.
Find the area of the part of the plane \(x+y+1\) in the first octant, as shown in the figure beolw.
Students may have difficulty representing the sides of the triangle as vectors. Encouraging them to represent the corners as vectors may help.
Students may have difficulty visualizing the triangle as half of a parallelogram -- and may forget the factor of \(\frac12\) even once they recognize the need for the cross product.
Some students will solve this problem geometrically, without vectors.
