The emergency exit is being indicated by a horizontal vector heading to the right
In the study of Algebra we learned that the subtraction of two real numbers, for example x and y, can be given as follows:
x – y = x + (-y)
Where –y is the opposite of y . In this way, for example:
7 – 3 = 7 + (-3) = 4
We define the subtraction of two vectors in a completely similar way, starting from the concept of opposite . Let’s consider a non-zero (non-zero) vector . The opposite of is a vector that has the same magnitude and the same direction, but has a direction opposite to the direction of the vector .
We indicate the opposite of by __ . In the figure above we have an example of a case where | | = 3 . Therefore, | __ | = 3 and __ have the opposite sense to . The opposite of the null vector is itself: .
Given then two vectors and , the difference between these two vectors is represented as follows:
And it can be defined by:
= + (- )
Let us see, for example, the case of the figure below and determine the vector such that
Therefore, we have:
= – = + (- )
In the figure above, we can see that the difference was obtained by adding with __ . However, it is easy to see that the vector could be obtained by connecting the ends of and as in case 3 of the figure above, with direction from B to A.
The addition and subtraction of vectors has been defined in such a way that we can work with vector equations in a similar way as we did with equations between real numbers, passing a term from one side to another, changing its sign.