This chapter is about the topic determine direction vector. This topic is part of the subject mathematics and belongs to the topic of vectors.
In the following sections we explain the most important terms on this topic and illustrate the whole thing with examples. At the end we have summarized the most important things about «determining the direction vector» for you!
Determining the direction vector – the basics first!
Before doing this, have a look at our article on the position vector. We assume that here as basic knowledge! ☺
What can you imagine by the direction vector?
First of all, to clarify the most important thing in advance: What is the directional vector anyway? Of the direction vectoralso called the connection vector, is the vector that connects two points.
And how can you now determine the direction vector?
In order to determine the direction vector or connection vector between the two points A and B, you have to divide the position vector that leads to point A from the position vector that leads to point B, subtract.
Maybe you heard the saying in math class «tip minus foot» come to hear, this is used in the determination of the direction vector. More on this in the following section.
The formula for calculation
Do you want the direction vector im two-dimensional spacei.e. from two points , calculate applies:
in the n – dimensional space with the points applies:
In general:
O indicates the origin of coordinates. denotes the position vector of the coordinate origin to point A and the position vector of the coordinate origin to point B.
Direction vector graphic representation
The following graphic shows you how you can imagine the connection vector in the coordinate system:
Let’s look at an example, then you will understand the whole thing even better!
Sample task 1 for determining the connection vector
Task:
Calculate the vector whose apex is at point A(3|-1) and whose foot is at point B(2|3).
Solution:
To get the direction vector, we plug the points into the formula described above:
Sample task 2 for determining the connection vector
Task:
Calculate the vector whose base is in point A(3|2|4) and whose top is in point B(2|1|2).
Solution:
To get the direction vector, we plug the points into the formula for n-dimensional space described above:
Determine direction vector – all important information at a glance
- Of the Direction vector or connection vector is the vector that connects two points.
- You can calculate this very easily with two given points. Remember the saying «tip minus foot».
- in the n – dimensional space with the points applies to the calculation:
Our recommendation for you
It is important to pay attention to which point is the toe point and which is the top point. Always keep the saying «tip minus foot» in mind. If you swap the tip and foot, you will get an incorrect result.