ACTIVITY 3.2
ARGUMENT OF A VECTOR

It is defined the argument of a vector, that we can consider with origin in the origin of coordinates, like the angle that he forms with the semi axis of the positive abscissas OX. In the figure you have four vectors respective arguments a, b, g and d.

The arguments use to express in grades or in radians, we will do it in grades. You observe that if the argument of a vector:

- is between 0º and 90º, the vector  is in the 1rst  quadrant
- is between 90º and 180º, the vector is in the 2nd quadrant
- is between 180º and 270º, the vector is in the 3rd  quadrant
- is between 270º and 360º, the vector is in the 4rth quadrant

We consider positive the angles traveled from OX in opposite way to the needles of the clock and negative, the angles in the same way.

Argument multiplicity. One same vector has infinite arguments: if is an argument between 0º and 360º, the other ones, differ in him in one or several circle turns, that is to say, in 360º or in a multiply, positive or negative, of 360º multiple. Therefore, 30º, 390º, 750º, -330º ..., can be arguments of one same vector.

INTERACTIVE ACTIVITY

This vector has module 3,5, that you can not vary, and argument 121,5º, that you can vary moving the green point.

1) Builds vectors with module 3,5 and with arguments:

2) Where are located the ends of all vectors that they have by module 3,5 if we draw all of them with the same origin?

SOLUTION

END OF ACTIVITY 3.2
ARGUMENT OF A VECTOR