It's all a useful generalization: Integrals are "multiplication, taking changes into account" and the dot product is "multiplication, taking direction into account".

How to compute the dot product of two vectors, examples and step by step solutions, free online calculus lectures in videos

The dot product between two vectors is based on the projection of one vector onto another. Let's imagine we have two vectors a a and b b, and we want to calculate how much of a a is pointing in …

It turns out there are two; one type produces a scalar (the dot product) while the other produces a vector (the cross product). We will discuss the dot product here.

Also, when writing a dot product we always put a dot symbol between the two vectors to indicate what kind of product we’re calculating. What is it good for? The answer to this question will be clearer after …

Jul 24, 2025 · The dot product, often referred to as the scalar product, combines two vectors to produce a scalar value. This operation assesses the extent to which one vector extends in the direction of …

Oct 17, 2024 · An example of a dot product is in a solar panel. To maximize efficiency, the rays coming from the sun should be perpendicular to the panels, that is, straight on.

Jul 2, 2025 · The dot product is a cornerstone of 3D computer graphics. It enables the computation of diffuse lighting, specular highlights, and occlusion effects, which are essential for rendering realistic …

The dot product (also sometimes called the scalar product) is a mathematical operation that can be performed on any two vectors with the same number of elements.

work is generally thought of as the amount of energy it takes to move an object; if we represent an applied force by a vector F and the displacement of an object by a vector s, then the work done by …