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.v=0, then u=0 or v=0

Answer 1

See explanation below.

Explanation:

False.

Counter example

Let's assume that we have two vectors u,v on a bidimensional space. Lets define u and v like this:

`u = (x,y)`

`v = (-y,x)`

We see on this case that
`u\\eq v, u \\eq 0 , v\\eq 0`. And for this case we have this:

`u.v = x*(-y) + y(x)  = -xy +xy =0`

We satisfy that the dot product is 0 but
`u\\eq 0 , v\\eq 0`

So then since not applies for this particular this statement is FALSE.