vectors

▶️ Watch on 3Speak In this video I go over the precise definition of a vector function limit and prove it in 2 different ways. The 1st s...

In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroida...

▶️ Watch on 3Speak In this video I go over an example on determining the vector function of the curve of intersection between a vertical...

In this video I go over an example on determining the vector function of the curve of intersection between a vertical cylinder and a sla...

In this video I go over an example in obtaining the vector and parametric equations of a line segment between two given points. I first ...

▶️ Watch on 3Speak In this video I go over an example in obtaining the vector and parametric equations of a line segment between two giv...

▶️ Watch on 3Speak In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of ...

In this video I go over the definition of the limit of a vector function, which involves taking the limit of each of its component funct...

In this video I introduce vector functions and show how they differ from the real-value functions that we are used to. Vector functions ...

In this video I deep dive nearly 5 hours into vector functions and space curves. A vector function has a domain (or input) of real numbe...

“Collinearity of vectors is the silent language of geometry, where lines speak in unison and points align with purpose.” — Unknown In ...

In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the dot and cross produc...

▶️ Watch on 3Speak In this video I show that if the dot or cross products are zero then neither vector has to be zero, but if BOTH the d...

In this video I show that a formula has different meanings when plotted in 2D vs 3D, such as the equation of a circle in 2D which become...

▶️ Watch on 3Speak In this video I quickly show that a vector is perpendicular to a plane if it is a multiple of the normal vector obtai...

▶️ Watch on 3Speak In this video I show two interesting formulas involving the dot and cross products in which a vector is used twice. T...

In this video I show that interchanging the vectors in the scalar triple product result in the same answer but not when doing so for the...

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 ...

▶️ Watch on 3Speak In this video I go over the physics of a solid block on an inclined plane in terms of the sliding friction, weight, n...

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

▶️ Watch on 3Speak In this video I find the largest sphere that passes through a given point while every point inside is also inside a l...

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 ge...

▶️ Watch on 3Speak In this video I find the sum of an infinite series of consecutive magnitudes of vector projections and show it turns ...

▶️ Watch on 3Speak In this video I determine the symmetric equations of a line at the intersection of two planes. I then find out that w...

▶️ Watch on 3Speak In this video I discuss how to determine the distance between two lines for each of the 3 possible cases: intersectin...

▶️ Watch on 3Speak In this video I go over a quick recap on the formula for determining the shortest distance between a point and a plan...

▶️ Watch on 3Speak In this video I illustrate a method for determining of 4 points lie on the same plane by checking if their scalar tri...

▶️ Watch on 3Speak 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...

▶️ Watch on 3Speak In this video I review how to determine whether two vectors or planes are parallel or perpendicular. Two vectors are ...

▶️ Watch on 3Speak In this video I go over the the 3 main equations of a line in 3D: vector equation, parametric equations, and symmetri...