projection of U onto v

I have used vector projections many times with computer graphics. A typical use is where I have an object on the screen that is at an angle, and the user clicks on the screen... and I want to know how far from an edge the use clicked.

The formula I would use is [ ( u dot v) / |v| ] * v

The answer I got is [21/ sqrt(10)] <-6,-2>

Unless I am missing something, the answer you gave from the book does not make sense since the answer must be parallel to <-6, -2> (or <3, 1>).

Let me know if this old guy missed something.

kingfish's equation for projection is correct, that is the vector projection

the scalar projection is simply the magnitude of the vector projection

ebrown, your equation is incorrect. it looks similar to the equation for scalar projection, however the last v term is extraneous

vector projection is a very simple concept.

Imagine a horizontal line extending to the right of the origin which we call vector A

Now imagine another line extended from the origin at a 45 degree angle in the first quadrant which we call vector B

Now shine a flashlight onto vector B and see where the shadow hits vector A...that is the projection.

Where does the flashlight beam originate from? It faces perpendicular to A because we're talking about the projection ONTO A. We're talking about coherent light rays by the way...the flashlight beam does not fan out.

stuh,

What is your calculation for the vector kingfisher gave?

The vector projection has the value of the "scalar" projection in the direction of the vector.

This means that if you find the scalar projection and multiply it by the unit vector parallel to v you will have the vector projection.

You are right, I made a mistake (I've been doing this in software too long) ... I multiplied by v instead of the unit vector.

[ ( u dot v) / |v| ] * v/|v|

(yes this looks like kingfishers original equation. His formatting was a bit confusing).

My calculations: u dot v = 42
|v| = 2 sqrt(10)

the scalar projection: 21/sqrt(10)

The unit vector: <-3, -1> / sqrt(10)

The projection: 21/10 <-3, -1> which is the same as -21/10 * <3,1>

Do you concur stuh?

yeah ebrown, that's right

I'm not sure what the "+ 17/10<-1,3>" term that kingfish mentioned is coming from

projection of u onto v,continued
Okay, I can get the first part, it is that second part that is driving me crazy! According to the answer in the back of the book the projection
of u onto v is -21/10 <3,1> + 17/10<-1,3> it is that 17/10 part that is my problem! I have no idea where it comes from.

All of the projection problems have a second part. I can't seem to figure it out. Glad to know I'm not the only one. Kingfish