Scalars vs. Vectors

About the lecture

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.

About the lecturer

Emille Lawrence is a Professor in the Department of Mathematics and Statistics at the University of San Francisco. She is a low-dimensional topologist and her mathematical interests include braid groups, geometric group theory, and spatial graphs. She is passionate about broadening participation in the mathematical sciences through outreach and mentoring. In 2021, Professor Lawrence received the Association for Women in Mathematics (AWM) Service Award for her work to increase diversity in those participating in the AWM.