ACTIVITY 2.1
COMPONENTS OF A VECTOR

In this unit we will see that a vector also can to come given as a pair of numbers. Define in the plan a coordinate system (one point origin, and two perpendicular axis). To every P point we associate a pair of numbers that are his coordinates (x,y), we write P (x,y). For example, A (1,2) and B(4,6).

Then, the vector is identified by the two following numbers:
- His first component, that is the number that it is necessary to add to A first coordinate to obtain B first coordinate; in our case, 3.
- His second component, that is the number that it is necessary to add to A second coordinate to obtain B second coordinate; in our case, 4.

We identify the vector with his components, and then we write = (3,4).

We can write  A+ = B, or good = B - A, that is a very comfortable way to get components of a vector if we know his origin in A and his extreme in B.

Also, we can see that two vectors are equal (that is to say, with the same direction and the same module) if and only if they have same components.

INTERACTIVE ACTIVITY

You move green points and you make the following constructions:

1) Draws a vector with origin in the point
A(-1,3) and end in the point B(2,-2).
Which are the components of the vector ?

2) Locate the point A in (-3, -2,) and later you locate B in a way that = (9,5).
Which are the coordinates of B?

3) Locate point B in (-7,5,) that is to say, B (-7,5), and later you locate A in a way that = (-8,11).
Which are the coordinates of A?

You check that it is always verified = B - A

SOLUTION

Given these six vectors

END OF ACTIVITY 2.1
COMPONENTS OF A VECTOR