Test Question: Vector Proof Help

[Dahaka14]

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

Homework Statement

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).

Homework 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)).

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?

 

[e(ho0n3]

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

 

[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.

 

[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.