Determine vector c, which is collinear vector of vector $a+b$, if $ab=5$, $cb=18$ and $|b|=2$.
I tried with $c=n(a+b)$.
$9= |c|*cos(\alpha)$...$|c|=\sqrt{(n^2(a+b)(a+b))}= n \sqrt{aa+14}$
Then $9= n \sqrt{aa+14}*cos(\alpha)$
Second equation is: $\frac{5}{2} \sqrt{aa}*cos(\alpha)$
From second equation we get: $cos(\alpha)=\frac{5}{2\sqrt{aa}}$. I put this in first equation and I get that $n=\frac{9\sqrt{14}}{35}$
My solution is: $c=\frac{9\sqrt{14}}{35}(a+b)$
Is this correct?
Thank you for your help.
$$n(a+b)b=18$$ or $$n(5+4)=18$$ or $$n=2,$$ which gives $$c=2(a+b).$$