Warm up 2

Warm up 2

Now, here is a question for you regarding the geometry of dot products, regarding kind of
visualizing what dot products mean.
Suppose I have a vector v over here and then I have vector u over here. And if I extend u
as a straight line, I can extend it until it makes a right angle with this vector. This would be
like making a right triangle here.
Then I have another vector that goes in the same direction as u and up to this point, where
the right triangle happens.

So that other vector is called w, and it's in the same direction as
u.
[Graph]
Which one is bigger? The dot product of u and v, or the dot product of u and w?
Three variants can be there. u dot v can be bigger, u dot w can be bigger, and of course
they can be equal.
Your task is to determine whether the two vectors shown in the picture are parallel based
on the geometry of the diagram and on what you know about dot products.