Find the value of $\frac{a+b+c}{d+e+f}$ Given real numbers $a, b, c, d, e, f$, such that:
$a^2 + b^2 + c^2 = 25$
$d^2 + e^2 + f^2 = 36$
$ad + be + cf = 30$
What is the value of $\frac{a+b+c}{d+e+f}$?
I've tried combining equations in several ways but haven't gotten very far. Any hints would be appreciated.

Hint:   by the Cauchy-Schwarz inequality:
$$
900 = 30^2 = (ad + be + cf )^2 \le (a^2 + b^2 + c^2 )(d^2 + e^2 + f^2) = 25 \cdot 36 = 900
$$
Equality occurs when $a,b,c$ and $d,e,f$ are proportional.
