What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

Mr. Andersen shows you how to draw free body diagrams of various objects. The major forces (like gravity, normal, tension, friction, air resistance, etc.) are discussed and then applied to various problems.

How do you think about a non-square matrix as a transformation?

What is a vector? Is it an arrow in space? A list of numbers?

What is a change of basis, and how do you do it?

How to think about matrix multiplication visually as successively applying two different linear transformations.

Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.

The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means.

Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.

How to think of 3x3 matrices as transforming 3d space

In this video Paul Andersen explains how a rotating system will have several quantities; including torque, angular velocity, angular acceleration and angular momentum. Each of these quantities have a vector property that can be...

This video recounts a lecture by Richard Feynman giving an elementary demonstration of why planets orbit in ellipses. See the excellent book by Judith and David Goodstein, "Feynman's lost lecture”, for the full story behind this lecture,...

How to think about matrix multiplication visually as successively applying two different linear transformations.

When you think of matrices as transforming space, rather than as grids of numbers, so much of linear algebra starts to make sense.

Continuing in our journey of understanding motion, direction, and velocity... today, Shini introduces the ideas of Vectors and Scalars so we can better understand how to figure out motion in 2 Dimensions. But what does that have to do...

In this video Paul Andersen explains how vector addition can be used to determine the electric field of a dipole.

Physicists, air traffic controllers, and video game creators all have at least one thing in common: vectors. But what exactly are they, and why do they matter? David Huynh explains how vectors are a prime example of the elegance, beauty,...

Drawing accurate free-body diagrams is essential for scoring points on the AP® Physics Exams. In this video, Mr. P, an actual AP® Physics Reader, shows you exactly how to draw free-body diagrams the way exam graders want to see them....

We will import two libraries, tfidf and cosine_similarity, and then use the TF-IDF vectorizer to generate chatbot responses based on the query input.

This content provides a step-by-step solution for calculating the torque on a particle about the origin, given its position vector and an applied force vector, using unit-vector notation. It then demonstrates how to find the angle...

This video demonstrates how to calculate the work done by a force and the power generated as an object moves through a given displacement over time. It provides a clear, step-by-step solution to a physics problem involving vectors.

How do you write the linear combination of unit vectors? How do you write the unit vector in the same direction as a given vector? What are the standard unit vectors? This video answers all of these questions and tells you all the basics...

How do you add vectors, subtract vectors, and use a scalar on vectors? This video shows how to do all of these vector operations both algebraically and graphically. This video is for a precalculus class

Find all six trig ratios given a point on the terminal side of theta. In this video we work this common type of problem. We use the Pythagorean Theorem to find "r" (hypotenuse), and then use the given "x" (adjacent) and "y" (opposite) to...