# United States Multivariable Calculus - Vectors in Three Dimensions

1. Dec 28, 2011

### GreenPrint

1. The problem statement, all variables and given/known data

See attachment

2. Relevant equations

3. The attempt at a solution

I'm not sure how to determine which points are co linear or which point lies in between the two. My book doesn't discuss how to do this at all.

but
PQ→ = <1,-1,2>, PR→ = <3,-3,6>
I believe I found these correctly but I'm not sure what to do from here. Thanks for any help anyone can provide.

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2. Dec 28, 2011

### Staff: Mentor

PR is a multiple of PQ. Doesn't that tell you something?

3. Dec 28, 2011

### GreenPrint

there parallel to each other but i don't know how that helps me answer the question

4. Dec 28, 2011

### tylerc1991

Imagine a similar setup in two dimensions. Suppose you are given three points, P, Q, and R in the x-y plane. Now suppose (as is the case in the original problem) that PQ is a multiple of PR. Try to make a graph of this scenario to convince yourself that the three points are colinear. Will this still be the case when we move up to three dimensions?

5. Dec 28, 2011

### GreenPrint

hm i didn't think of it like that interesting
ok so they are indeed co linear then
can i find the magnitude of pq and pr and then just compare which one is smaller to determine if q lies in between p and r or if r lies between p and q?

6. Dec 28, 2011

### tylerc1991

Yes. You will compare distances to determine which point lies between the other two. Be sure to use the two dimensional analogy again if you get stuck (and keep it in mind for future problems ).

7. Dec 28, 2011

### GreenPrint

thanks for your help