# vectors, solving geometrically

• February 7th 2011, 11:58 AM
centenial
vectors, solving geometrically
I've had a bunch of these type of problems come up, and I'm at a loss to how to go about solving them. Maybe someone could show me a direction to start in?

http://img715.imageshack.us/img715/7563/136i.png

I know that because the vectors v1 and v2 are parallel, then the dot product of v1 and v2 = 0. But, I'm not sure how to relate that to the problem.

Any help would be appreciated. Thanks!
• February 7th 2011, 12:10 PM
TheEmptySet
Quote:

Originally Posted by centenial
I've had a bunch of these type of problems come up, and I'm at a loss to how to go about solving them. Maybe someone could show me a direction to start in?

http://img715.imageshack.us/img715/7563/136i.png

I know that because the vectors v1 and v2 are parallel, then the dot product of v1 and v2 = 0. But, I'm not sure how to relate that to the problem.

Any help would be appreciated. Thanks!

First if the vectors are parallel then their dot product is not zero. It is the product of their lengths. Perpendicular vectors have a dot product equal to zero.

Here is the question when we add vectors in $\mathbb{R}^2$ we use the parallelogram law.
Since $\vec{v_1},\vec{v_2}$ are parallel their sum will ALWAYS be parallel to both $\vec{v_1},\vec{v_2}$. So the question is can you draw a parallelogram with sides $\vec{v_1},\vec{v_2}$ and get $\vec{v_3}$ as the diagonal?
• February 7th 2011, 12:19 PM
centenial
Thanks, I think I understand. So, since $\vec{v_1},\vec{v_2}$ are parallel, it's not geometrically possible to draw $\vec{v_3}$ in such a way that it is the diagonal of the parallelogram $\vec{v_1},\vec{v_2},\vec{v_3}$. In fact, because they are parallel, there is no such parallelogram.

Is that correct?
• February 7th 2011, 12:21 PM
TheEmptySet
Yes that is the idea.