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$r$, $a$, $b$ 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.

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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
up vote 1 down vote accepted

I will denote vectors by boldface. I am not sure I understood the problem correctly. (Why is it tagged cross product? The cross product does not appear in the formulation of your problem.)

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 $$\mathbf b.\mathbf n - \alpha \mathbf a.\mathbf n =3$$ $$\alpha=\frac{\mathbf b.\mathbf n-3}{\mathbf a.\mathbf n}$$

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Thanks a lot for the answer. Sorry for tagging it cross-product, but I didn't find dot-product in the list. – Sorin Cioban Apr 15 '11 at 20:22

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