Vectors and the Geometry of Space: True-False Quiz https://youtu.be/8q0up5ccko8

In this video I go over the end-of-chapter True-False Quiz as a review for the Vectors and the Geometry of Space chapter.  There are 22 questions in total covering vectors, cross products, dot products, lines, surfaces, and much more.

Problems Plus 8: Volume of a Solid from its Shadows https://youtu.be/S-MGdEU9DF0

In this video I obtain the volume of the largest solid whose shadows are a square of height 1, a circle, and an isosceles triangle.

Problems Plus 7: The Physics of a Block on an Inclined Plane https://youtu.be/0ZJPy-Egfpk

In this video I go over the physics of a solid block on an inclined plane in terms of the sliding friction, weight, normal force, and applied horizontal force.

Problems Plus 6: Largest Sphere in a Sphere https://youtu.be/uefSE-rXFw4

In this video I find the largest sphere that passes through a given point while every point inside is also inside a larger sphere.

Problems Plus 5: Infinite Sum of Vector Projections is a Geometric Series https://youtu.be/rKt2qVLCMiM

In this video I find the sum of an infinite series of consecutive magnitudes of vector projections and show it turns out to be just a geometric series.

Problems Plus 3: Line and Surface of Two Intersecting Planes https://youtu.be/jj3wYCYhhq8

In this video I determine the symmetric equations of a line at the intersection of two planes. I then find out that when the equations of the plane vary, the line sweeps out a circular hyperboloid of one sheet. Finally, I calculate the volume of this surface between two planes.