ACTIVITY 5.1
DEFINITION OF SCALAR PRODUCT OF TWO VECTORS

The scalar product of two vectors and is a scalar that it is defined like the product of their two modules by the cosine of the angle that they form.

The scalar product of and expresses·(for this reason, it is sometimes called dot product). If we agree that expresses the angle that form and , we can write:

·= || || cos()

Observe that the scalar product of two vectors it isn't another vector. The same as its name indicates, is a scalar. Surely, later is will be able to explain another type of product of vectors, it is called vectorial product, where the result is another vector.

Like you see in the figure, two vectorsand form two angles. If one is , the other is 360º -. With we'll indicate the most little of the two possible angles ( or 360º - ). In fact, this election hasn't importance when we calculate the scalar product ofandbecause
cos = cos(360º - ).

INTERACTIVE ACTIVITY

You have a construction in order to practice with the scalar product of two vectors and .

1) Calculate the scalar product of two vectors and of modules with respect to 6 and 10, and they form an angle of 45º.

2) Check that the scalar product can be negative.

3) Try to get a situation where the scalar product coincides with the product of the modules, that is to say:
               · = ||||

4) And a situation where · = - ||||?

SOLUTION

END OF ACTIVITY 5.1
DEFINITION OF SCALAR PRODUCT OF TWO VECTORS