Vectors on the ACT® Math: Complete Guide
Read time: 2 minutes Last updated: September 23rd, 2024
Vectors are another topic on the ACT® Math section that has increased in importance in the last 5 years. A vector is a quantity that has both magnitude (size) and direction, often represented by an arrow.
The questions the ACT® Math section asks about vectors are relatively straightforward. You need to know a few basic facts about vectors. Beyond that, these questions often, but not always, boil down to basic arithmetic.
Vector Addition Example
Vectors u = <2, 3> and w = <-4, 1>. What is u + w?
In vector notation, the angle brackets < > represent the components of the vector. The first number is the x-component, and the second is the y-component.
- Add the x-components: 2 + (-4) = 2 - 4 = -2
- Add the y-components: 3 + 1 = 4
Combine the Results:
So, the sum of vectors u and w is: u + w = <-2, 4>
Graphing Vectors
When the ACT® Math section asks you to graph vectors, it's the same thing that we see in a graph question.
Graph the following vectors: t = <2i + 3j>, v = <-4i + 1j>
In vector notation, i represents the unit vector in the x-direction (horizontal), and j represents the unit vector in the y-direction (vertical). So, 2i means 2 units in the x-direction, and 3j means 3 units in the y-direction.
To graph a vector, follow these steps:
- Start at the origin (0,0).
- Move horizontally by the number of units indicated by the i-component.
- From that point, move vertically by the number of units indicated by the j-component.
- Draw an arrow from the origin to the final point.
The direction of the arrow indicates the direction of the vector, and the length of the arrow represents the magnitude of the vector.
Vector t = <2i + 3j> in red
- x-component (horizontal) is +2
- y-component (vertical) is +3
This means the arrow points to the right and upwards, from the origin (0, 0) to the point (2, 3).
Vector v = <-4i + 1j> in yellow
- x-component (horizontal) is -4
- y-component (vertical) is +1
This means the arrow points to the left and slightly upwards, from the origin (0, 0) to the point (-4, 1).
Real-World Applications of Vectors
Vectors can also be useful in real life. Engineers use them to design bridges that can withstand wind forces. Video game developers use vectors to create realistic motion in games. Even your smartphone uses vector calculations for GPS navigation.