# Find r in terms of a, b and n for:

$r$, $a$, $b$ and $n$ are vectors; I need to find $r$ in terms of the others for

(1) $r\cdot n = 3$;

(2) $r + \alpha\cdot a = b$.

Could anyone please give me a hint on how to start? I thought about doing the dot product of the second equation with $n$, but it didn't help too much.

There may be no solution.

-
What is alpha? Is ti vector/number? Is it given? –  Martin Sleziak Apr 15 '11 at 18:40
Alpha is a constant. –  Sorin Cioban Apr 15 '11 at 18:56
Making the question more precise can be helpful. –  Jack Apr 15 '11 at 19:26
I just need to solve the pair of equations. –  Sorin Cioban Apr 15 '11 at 19:29

From the second equation you get $$\mathbf r=\mathbf b-\alpha.\mathbf a.$$ Thus once you have determined $\alpha$, you get $\mathbf r$ from this equation.
Plugging this into the first equation yields $$\mathbf b.\mathbf n - \alpha \mathbf a.\mathbf n =3$$ $$\alpha=\frac{\mathbf b.\mathbf n-3}{\mathbf a.\mathbf n}$$