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. At an incline angle just before the block

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

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

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. - notes - playlist

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. I first calculate the magnitudes for the first few

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

In this video I discuss how to determine the distance between two lines for each of the 3 possible cases: intersecting lines, parallel lines, and skew lines. If two lines intersect, their distance is zero,

In this video I go over a quick recap on the formula for determining the shortest distance between a point and a plane in 3D. The formula is just the projection of any position vector from the plane to

In this video I illustrate a method for determining of 4 points lie on the same plane by checking if their scalar triple product (or volume of a parallelepiped) is zero. If it is zero then it means the

In this video I go over a method for determining if 3 points lie on the same line by using the cross product of any 2 position vectors formed from the points. If the cross product is zero then the points

In this video I review how to determine whether two vectors or planes are parallel or perpendicular. Two vectors are parallel of their cross product is zero, and are perpendicular if their dot product

In this video I go over the the 3 main equations of a line in 3D: vector equation, parametric equations, and symmetric equations. The vector equation defines a line as a vector to a point on the line and

In this video I show that we can determine the angle between two intersecting planes by computing the dot product of their normal vectors. This follows from the dot product formula being equal to their

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

In this video I go over a quick review of the formulas for the scalar and vector projections of one vector onto another, as well as showing their visual representations. The scalar projection of a vector

In this video I review the dot product formulas and its useful properties such as finding the angle between vectors and calculating work done on an object by a constant force. The dot product is the

In this video I go over a quick review of the basics of vector algebra, namely the definitions of vectors vs scalars, and their addition or multiplication. A vector is a quantity that has both a magnitude

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In this video I start off with the linear equation of a plane and go backwards to show that, if at least one of a, b, and c are not zero, then the equation does indeed represent a plane. I show this by

In this video I go over determining the distance between skew lines, which are lines that are not parallel and don't intersect. To determine this, we can first interpret the skew lines as being on two