Test Question: Vector Proof Help

1. Feb 27, 2008

Dahaka14

Sorry for notation guys, but I don't know how to use LaTex.

1. The problem statement, all variables and given/known data
True or false, there exists a vector v (or set of vectors) in R3 such that v*v = ||v|| (v dot v equals the magnitude of v).

2. Relevant equations
At first I thought this was false, but then I considered an arbitrary unit vector v=(1/(14)/\(-1/2)*(1,2,3)...in words: one over the square root of fourteen times the vector one, two, three (the unit vector of (1,2,3)).

3. The attempt at a solution

Taking v*v, u get (1*1)/14 + (2*2)/14 + (3*3)/14 = 1/14 + 4/14 + 9/14 = 14/14 = 1, which is trivial for a unit vector. Also, the magnitude is just the square root of this answer, since the components are already squared for dotting itself, which is one; again, trivial. Am I correct or can I not consider a unit vector?

2. Feb 27, 2008

e(ho0n3

You just demonstrated that the answer it true. Why are you doubting yourself?

3. Feb 27, 2008

Dahaka14

I am doubting myself because I had strong opposition from 3 classmates that for some reason you can't use a unit vector for the proof.

4. Feb 27, 2008

Mystic998

Well, we can't really tell you if it said that you can't use unit vectors. Regardless, it's clearly true for any unit vector because, using your notation, the equation says ||v||^2 = v*v = ||v||.

Edit: Yeah, I'm really out of it today.

Last edited: Feb 27, 2008