Problem 11.5.106 - Finding the angle between two sides of a container. - Calc III HW Help

This is problem 11.5.106 from the Larson and Edwards' Calculus: Transcendental Functions text. In this problem, we were given side lengths for a container, and we were asked to find the angle between two adjacent sides. Solving the problem requires superimposing a coordinate system, finding vectors on each side, using cross product to find the normal vector to the plane containing each side, and finally using the geometric definition of the dot product to find the angle between the normal vectors, which is the same as the angle between the adjacent sides.
We had to assume that the top and bottom of the container lie in parallel planes, and that the 6 inch by 6 inch bottom of the container was centered inside the 8 inch by 8 inch top of the container.

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I said a couple things incorrectly in this video. I said that the vector in the front and back are parallel and the same, but that’s not accurate. The vectors would have the same length due to the symmetry assumptions we made, but their directions would be different. Those inaccurate statements don’t affect the component forms of the vectors u, v, or w though, so the solution to the problem is still correct.