Intro To Vectors

Vectors can be used to represent many things and in many different ways. This makes them incredibly useful, but also fairly confusing to a first time user… but if you want to do physics, engineering or simply pass Math SL then you're going to need to learn something about them.

Two Types of Quantities

Scalar Quantities - Quantities that only have "magnitude" or size. Things such as mass (kg) or temperature.

Vector Quantities - Quantities that have both direction and magnitude. Such as velocity (moving at 10 kph to the west) or force (10N down).

Its worth noting that the term "magnitude" gets used a lot with vectors. It essentially a fancy word for size or length. We'll talk more about it later.

Different Vector Representations

Vectors get represented in many different ways. I have listed and attempted to describe the 4 that the IB uses below.

Directed Line Segments or "Arrows"

This is probably the easiest to understand and most intuitive representation of vectors.

Column Representation

The most common representation in Math SL.

Unit/Base Vectors

In my experience this was the most common representation used in university level physics. It's my personal favorite, but doesn't show up on exams too often.

What the IB calls "Position Vectors"

Used frequently along with column representation. These vectors often do not start at the origin.

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