Question

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disaproves the statement.

If u and v are in V3, then |u.v|<-|u|.|v|

Answer 1

This statement is true for any N vectorial space.

By definition u·v=|u|·|v|·cos(α), where α is the angle between u and v.

If -1≤cos(α)≤1, we can assume:

|u·v|=||u|·|v|·cos(α)|=|u|·|v|·|cos(α)|≤|u|·|v|