# Thread: Dot Product and parallel

1. ## Dot Product and parallel

u=i+j v=ai-j they are parallel and I need to solve for a

I have no idea how to do it and any help would be greatly appriciated

2. Parallel vectors are multiples of each other.
Does $\displaystyle a = -1$ work?
WHY?

3. thanks a lot .

i see that it works because then you have 2=-2, but i don't understand how you get it...

4. Originally Posted by carly_1026
thanks a lot .

i see that it works because then you have 2=-2, but i don't understand how you get it...
Two vectors $\displaystyle \vec u$ and $\displaystyle \vec v$ are collinear (vulgo parallel) if

$\displaystyle k \cdot \vec u = \vec v~,~k \in \mathbb{R}$

Therefore:

$\displaystyle k \cdot (i + j) = ai - j~\iff~ ki +kj = ai -j~\iff~ ki = ai\ \wedge \ kj = -j$

From the last equation you get:

k = -1 . Plug in this value into the equation ki = ai and you'll get a = -1