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
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