How to visualize quaternions, a 4d number system, in our 3d world

What Cramer's rule is, and a geometric reason it's true

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

How to visualize quaternions, a 4d number system, in our 3d world

How to think about this 4d number system in our 3d space.

The third and final part of the block collision sequence.

The third and final part of the block collision sequence.

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

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

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

This rule seems random to many students, but it has a beautiful reason for being true.

Divergence, curl, and their relation to fluid flow and electromagnetism

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

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

Intuitions for divergence and curl, and where they come up in physics.

Divergence, curl, and their relation to fluid flow and electromagnetism

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.

Understand how the dot product of two vectors yields a scalar quantity and how scalar multiplication affects vector direction and magnitude. Explore the formula, geometric meaning, and unit vector method to calculate dot products in...

Learn how to calculate work done when force is applied at an angle to displacement. Explore vector components, dot product, and how angle affects positive, negative, or zero work in this essential Class 11 Physics lesson.

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...

We've looked at a few simple examples of first-order differential equations and how to solve them. Now let's take a look at exact first-order differential equations.

JAX is a Python library similar to NumPy for scientific computing and linear algebra, but designed to run on accelerators like Cuda-based GPUs and Google's TPUs.

In this video, you will apply what you have learned about classes through a practical exercise. You will be given a problem statement and will learn how to design and implement a class to solve the problem. This exercise will help you...