1. ## Norm of Vectors

I feel like this is a really stupid question but I just can't figure out how to solve it:

If ||u|| = 2 and ||v|| = and u (dot) v = 1, find ||u (dot) v||

Thanks for the help!

2. Originally Posted by Laydieofsorrows
I feel like this is a really stupid question but I just can't figure out how to solve it:

If ||u|| = 2 and ||v|| = and u (dot) v = 1, find ||u (dot) v||

Thanks for the help!

It's not stupid but something's wrong here: both the dot product and the norm are defined for vectors (the first one for two, the second one for one) and give back a scalar (a number), so ||u (dot) v|| is the norm of a scalar, not a vector, and this doesn't make much sense. Read carefully the question again.

Tonio

3. I checked the problem and it's correct.

Can I get another opinion?

4. Originally Posted by Laydieofsorrows
I checked the problem and it's correct.

Can I get another opinion?

I suppose you can get a million opinions yet the question still makes no sense as given. If you're not giving all the data then do.

Tonio

5. Originally Posted by Laydieofsorrows
I checked the problem and it's correct.

Can I get another opinion?
You can trust tonio, he's an expert. Seriously, if the question is as stated then either it's a trick question or there's a mistake in it. If the norm of a scalar means anything at all, then it must just mean the absolute value. So if u (dot) v = 1, then ||u (dot) v|| = 1.

6. Is it possible that the problem asked for $||u\times v||$, the norm of the cross product of u and v?

If so, you could use the facts that $|u \cdot v|= ||u||||v||cos(\theta)$ and $||u\times v||= ||u||||v|| sin(\theta)$, where $\theta$ is the angle between u and v.

Since you are given that $|u\cdot v|= 1$ as well as the values of ||u|| and ||v||, you can solve for $cos(\theta)$. Use that to find $\theta$ (which must be between 0 and $\pi$) and then find $sin(\theta)$.