Answer:
Substitute the results of the calculation into kv + u:
( 5.3, 2.68)T + (-2.1, 4.32)T = (3.2, 7.0)T, = w as expected.
Substitute the results of the calculation into kv + u:
( 5.3, 2.68)T + (-2.1, 4.32)T = (3.2, 7.0)T, = w as expected.
The point of all this is for you to get a gut-level understanding of what is going on when one vector is projected onto another. This, as previously mentioned, is constantly occuring when a computer is displaying graphics. Much of the calculation takes place in the computer's graphics hardware. Millions of vectors are projected per second. If you want to know what is going on with computer graphics, this is something you need to know.
Here is a new problem. Find the projection of w onto v:
You are not going to make your living actually doing these calculations. And I have a headache from setting all these equations in HTML. So skip the math and just read off the answer from the diagram.
w = ( ________ , ________ )T v = ( ________ , ________ )T kv = ( ________ , ________ )T u = ( ________ , ________ )T
Fill in the blanks. Perhaps the back of an envelope would be useful.