Calculus 3 Lecture 11.1: An Introduction to Vectors: Discovering Vectors with focus on adding, subtracting, position vectors, unit vectors and magnitude.

We can multiply a force by a scalar thus increasing or decreasing its strength. Position, displacement, velocity, acceleration, force, and momentum are all physical quantities that can be represented mathematically by vectors. The set of vectors and the two operations form what is called a vector space.

Feb 16, 2025 · Our examples have illustrated key principles in vector algebra: how to add and subtract vectors and how to multiply vectors by a scalar. The following theorem states formally the properties of these operations.

Just like every other topic we cover, we can view vectors and matrices algebraically and geometrically. It is important that you learn both viewpoints and the relationship between them. Part A: Vectors, Determinants, and Planes. Part B: Matrices and Systems of Equations. Part C: Parametric Equations for Curves. Exam 1. Next »

This section provides materials for a session on vectors, including lecture video excerpts, lecture notes, a problem solving video, worked examples, and problems with solutions.

As examples of vectors we may mention velocity, momentum, force, and acceleration. For many purposes it is convenient to represent a vector quantity by an arrow that indicates the direction in which it is acting.

Lecture 1 Introduction to vectors and tensors Instructor: Prof. Marcial Gonzalez What is a tensor? - Tensors are abstract mathematical entities. - Vectors are first order tensors.

Lecture 1: What Is A Vector?

In orthogonal coordinate systems, each vector can be ex-pressed as a linear combination of unit vectors representing the directions of the orthogonal axes, also referred to as the basis vectors.