Lesson 1 of 8
What is a vector?
A vector is an ordered list of numbers. Learn to read its components and draw it as an arrow.
The idea
A vector is an ordered list of numbers. Each number is called a component. In this course our vectors have two components, so we call them 2D vectors.
Here is a vector called v. You will see it written in two ways, which mean exactly the same thing:
In the column form, the first component is on top and the second component is underneath. Here the first component is 3 and the second component is 2.
Order matters
Swapping the components gives a different vector. The vector (3, 2) and the vector (2, 3) contain the same numbers, but in a different order, so they are not equal.
A vector as an arrow
You can draw a 2D vector as an arrow that starts at the origin, the point where the two axes cross. The first component tells you how far to move across: right for positive, left for negative. The second component tells you how far to move up for positive, or down for negative.
The arrow for v = (3, 2) moves 3 squares right and 2 squares up.
Equal vectors
Two vectors are equal when their first components are equal and their second components are equal. That simple rule lets you find unknown numbers.
Worked example
These two vectors are equal:
Find a and b.
Match the components
The first components must match, so aequals4.
The second components must match, so bequals5.
Check
With these values, both sides become the same vector:
the vector with components 4, 5
Common mistakes
- Reading the column from the bottom. The first component is always the top one.
- Treating (3, 2) and (2, 3) as the same. The order of the components is part of the vector.
- Drawing the second component across. First is across, second is up or down.