1. ## [SOLVED] Vector Proof

Prove that if u is parallel to v then |u · v| = |u||v|.
Prove that if
u is not parallel to v then |u · v| < |u||v|.

Can anyone help me prove this please

2. Originally Posted by the1u2001
Prove that if u is parallel to v then |u · v| = |u||v|.
Prove that if
u is not parallel to v then |u · v| < |u||v|.

Can anyone help me prove this please

Thanks Muqtasid

recall, $\bold{u} \cdot \bold{v} = |\bold{u}||\bold{v}| \cos \theta$

where $\theta$ is the angle between the vectors

what does $\theta$ have to be for the vectors to be parallel? what does it have to be for them not to be parallel? how does this affect the dot product

3. Originally Posted by Jhevon
recall, $\bold{u} \cdot \bold{v} = |\bold{u}||\bold{v}| \cos \theta$

where $\theta$ is the angle between the vectors

what does $\theta$ have to be for the vectors to be parallel? what does it have to be for them not to be parallel? how does this affect the dot product

u is parallel to v if and only if the angle between u and v is 0 or (pie/2).

4. Originally Posted by the1u2001
u is parallel to v if and only if the angle between u and v is 0 or (pie).

yes, and what happens in those two case, in particular, what is $\cos \theta$? can you answer the problem now?

5. Originally Posted by Jhevon
yes, and what happens in those two case, in particular, what is $\cos \theta$? can you answer the problem now?

I understand what happens but i don't know where to start with the proof

6. Originally Posted by the1u2001
I understand what happens but i don't know where to start with the proof
start with the formula i gave you. say what theta has to be if the vectors are parallel and plug the values in and show what happens.

then say what theta has to be for the vectors not to be parallel and show what happens.

pretty straight forward stuff. don't fall into the trap of making this more complicated than it already is just because the word "prove" is there.

you may also want to say, $0 \le \theta \le 2 \pi$

7. Originally Posted by Jhevon
start with the formula i gave you. say what theta has to be if the vectors are parallel and plug the values in and show what happens.

then say what theta has to be for the vectors not to be parallel and show what happens.

pretty straight forward stuff. don't fall into the trap of making this more complicated than it already is just because the word "prove" is there.

you may also want to say, $0 \le \theta \le 2 \pi$
K thank for the help and i have proved that if u is parallel that theta=0

but i am find it difficlut for if U is not parallel. is

theta

8. Since the two vectors are not parallel, i.e. $\theta \neq 0, 2\pi$, then that must mean $\cos \theta < 1$. Can you see how to get inequality $\bold{u} \cdot \bold{v} < |\bold{u}||\bold{v}|$ from $\bold{u} \cdot \bold{v} = |\bold{u}||\bold{v}|\cos \theta$ now?

9. Originally Posted by o_O
Since the two vectors are not parallel, i.e. $\theta \neq 0, 2\pi$, then that must mean $\cos \theta < 1$. Can you see how to get inequality $\bold{u} \cdot \bold{v} < |\bold{u}||\bold{v}|$ from $\bold{u} \cdot \bold{v} = |\bold{u}||\bold{v}|\cos \theta$ now?

Yes know i get it, thanks for the Help. I really appriate it.