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|

Question

Gage Mccarty

Mathematics

27 April, 17:34

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|

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Answers (1)

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Carissa Ferrell · 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|

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|

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|