0
$\begingroup$

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

  • 0
    I just need to solve the pair of equations.2011-04-15

1 Answers 1

1

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

  • 0
    Thanks a lot for the answer. Sorry for tagging it cross-product, but I didn't find dot-product in the list.2011-04-15