Geometry in the plane

# scalar product

The **scalar or dot product** of two vectors, *u* and *v*, is the number:

Example: *u*(1,2);*v*(3,-2)*u · v* = 3 – 4 = -1

Then, the **angle between two vectors** is:

In the example:

Two vectors, *u* and *v*, whose dot product is 0, are said to be **orthogonal**. Then the angle between them is 90^{0}.

**NOTE**: an orthogonal vector to *u(u _{1},u_{2})* is

*(-u*

_{2},u_{1})* *

**Exercises: **If *u(3,1), v(-2,2), w(-3,t)*, then:

a) Calculate *u·v*

b) Calculate the angle between *u* and *v*

c) Calculate *t*, to make *v* and *w* orthogonal.

Solutions: a) -4; b) 116º33'54''; c) -3

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