VTMO 2019 — Grade 7 — final Question 2

$a$)Given $\frac{bz - cy}{a} = \frac{cx - az}{b} = \frac{ay - bx}{c}$ for nonzero real $a , b , c$, prove $\frac{x}{a} = \frac{y}{b} = \frac{z}{c}$. $b$)If six-digit abcdef is divisible by $7$, prove efabcd is divisible by $7$.