Scalars vs. Vectors

Vectors

In the course, Professor Emille Lawrence (University of San Francisco) explores vectors. In the first mini-lecture, we discuss the difference between scalars and vectors, understand what it means for a vector to have magnitude and direction, and look at examples that illustrate important properties of vectors. In the second mini-lecture, we introduce vector arithmetic, specifically adding vectors, scalar multiplication, and subtracting vectors. In the third mini-lecture, we learn how to represent vectors in 2D and 3D spaces, assign components to vectors, and define position vectors. In the fourth mini-lecture, we discuss how to calculate the magnitude of a vector and how to find the distance between vectors. Finally, in the fifth mini-lecture, we introduce unit vectors and normalisation.

Scalars vs. Vectors

In this mini-lecture, we discuss the difference between scalar quantities and vector quantities, focusing in particular on: (i) how scalar quantities describe magnitude (size); (ii) examples of scalars, such as time, distance, and mass; (iii) how vector quantities describe magnitude and direction; (iv) examples of vector quantities, such as velocity, force, weight, acceleration; (v) geometric vectors, which are vectors with a specified initial point and terminal point; (vi) a given vector’s length, which illustrates its magnitude, and the vector’s direction, given by the direction the arrow is pointing; (vii) an example of a vector describing a real-world displacement: a ship sailing northeast from point A to point B; (viii) two types of vector notation; (ix) two examples showing that vectors with the same magnitude and direction are the same vector, even if they are at different positions; and (x) the zero vector, which has no length and no direction.