- #1

- 37

- 3

- Homework Statement
- Let ##\vec{e}## be a unit vector so that ##\vec{e}^2 = 1## and let ##\vec{v} = 3\vec{e}##.

Show that ##\hat{v} = \vec{e}## and ##|v| = \vec{v}\vec{e} = 5##

- Relevant Equations
- ##\vec{x} = |x|\hat{x}##

Not sure how to show that because ##\vec{v} = |v|\hat{v} = 3|e|\hat{e}##, but since ##\vec{e}## is a unit vector we know ##|e| = 1## so our equation now becomes ##\hat{v} = \frac{3\hat{e}}{|v|}##. So, we're left to the task of showing that ##|v| = 3## in order to conclude that ##\hat{v} = \vec{e}##.

Another way I tried to do it was ##\vec{v}^2 = |v|^2\hat{v}^2= 9\vec{e}^2## which implies that ##|v|^2 = 9## or ##|v| = 3##

However, if this is true, the second part can't be true i.e ##|v| = 3 \neq 5##

So, either there is a typo in the problem, or I'm interpreting the first part that since ##\vec{e}## is a unit vector, that ##|e| = 1##

The questions that follow up on this have it being that ##|v| = 5## which makes since for the second part, but I can't see how both of these can be true.

Thanks for your help!

Another way I tried to do it was ##\vec{v}^2 = |v|^2\hat{v}^2= 9\vec{e}^2## which implies that ##|v|^2 = 9## or ##|v| = 3##

However, if this is true, the second part can't be true i.e ##|v| = 3 \neq 5##

So, either there is a typo in the problem, or I'm interpreting the first part that since ##\vec{e}## is a unit vector, that ##|e| = 1##

The questions that follow up on this have it being that ##|v| = 5## which makes since for the second part, but I can't see how both of these can be true.

Thanks for your help!