Lecture 2 | Vectors

Vector Operations

Lecture 2 | Vectors

Vector Operations

A vector is a mathematical object with both direction and magnitude. Vectors are visualized by an arrow, where the arrow's point represents the direction and its length represents the magnitude. Vectors can be added to other vectors and multiplied (or scaled) by numbers, known as scalars.

Why use these mathematical objects, and how might you have seen them before? Any time you give someone directions you are describing a vector, ie, "go southeast (direction) 50 steps (magnitude)". In physics, you will see vectors used to describe motion, gravity, electricity, magnitism, and much more.

Now, check out Vector's description of a vector (from Despicable Me).

Vector's description of a vector (Despicable Me)

Pre-lecture Study Resources

Read the BoxSand Introduction and watch the pre-lecture videos before doing the pre-lecture homework or attending class. If you have time, or would like more preparation, please read the OpenStax textbook and/or try the fundamental examples provided below.

Review and Vectors | Vector Operations

Vectors can be used to represent anything that has a direction and magnitude, such as velocity, acceleration, forces, displacement, or electric and magnetic fields.

Scalars are just a number, and can represent speed (magnitude of velocity), time, temperature, and distance (magnitude of displacement.

Here are some ways to represent vectors:

Cartesian (component): $\overrightarrow{A} = \langle A_x, A_y, A_z \rangle$

Image of cartesian

Polar: magnitude and (angular) direction $(|\overrightarrow{A}|,\theta)$

We have focused so much on creating introductions to the physics content we haven't had time to create text that reviews vectors. We do however have good videos on what you'll need to know starting this class. Check them out below in the drop down called BoxSand Videos. You can also check out the vectors sections of the OpenStax Textbook in the drop down below.

Required Videos

Vector Representations

Vector Addition

Suggested Supplemental Videos

How Not to Suck at Physics (8min)

How Not to Suck at Physics Part 2: Challenge Homework

Section 3.2 of the OpenStax text book provides additional understanding of graphical methods of vector operations.

Section 3.3 of the OpenStax text book covers analytical methods of vector component decomposition and vector operations like addition and subtraction.