Notice that the projection of w onto v does NOT depend on
the length of v.
Only the direction of vector v affects the results.
The length of the projection is
(These are not facts to be memorized; the idea is to practice visualizing what is going on by thinking about such things). And nothing better for visualization than another example.
Project w onto v by examining the diagram. (To make this example especially hard, I've changed the colors.)
w = ( ________ , ________ )T v = ( ________ , ________ )T kv = ( ________ , ________ )T u = ( ________ , ________ )T