the amplitude of the sum of two vectors

Question

$X=(x_1,x_2,...,x_n)$, $Y=(y_1,y_2,...,y_n)$ and $Z=aX+Y$, $a>0$.

If $a$ increases, would $\max(Z)-\min(Z)$ increase? i.e., is $\max(Z)-\min(Z)$ a non-decreasing function of $a$?

$X$ and $Y$ are real numbers.

Thanks.