ACTIVITY 3.7
OBTAINING VECTORS OF MODULE 1 (UNIT VECTORS)

Next we will explain an easy way to get a vector that it will have the same direction that the other vector, but whose have module 1.

If they give us a vector and we divide him by his module (that is to say, we multiply him by ), we get the vector =  which has the same direction and way that , but it has module 1:

For instance, if =(3,4), then ||=5, and vector = =( ³/₅,⁴/₅) has module 1, like you can check easily.

If we would have interested in a vector of module 1 with opposite direction that , it's enough with calculating the opposite to = , that is to say, the vector = - .

Vectors of module 1 are called unit vectors or versors.

INTERACTIVE ACTIVITY

In the applet of the right side you have a vector and the unit vectors =    and = -  with the same direction and with opposite direction to respectively.

You get untied vectors and from the next vectors . Moving the end A of the vector , draw them in the applet and check the results:

a) = (4 , 3)	e) = (-2 , 2)
b) = (0 , 3)	f ) = (0 , -2)
c) = (-2 , 1)	g) = (4 , -1)
d) = (-3.5 , 0)	h) = (4 , 0)

SOLUTION

END OF ACTIVITY 3.7
OBTAINING VECTORS OF MODULE 1 (UNIT VECTORS)