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 90⁰.

NOTE: an orthogonal vector to u(u₁,u₂) is (-u₂,u₁)

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