The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is

A line $L$ passes through the points $(1,2,-3)$ and $(\beta, 3,1)$ and a plane $\pi$ passes through the points $(2,1,-2)$, $(-2,-3,6),(0,2,-1)$. If $\theta$ is the angle between the line $L$ and plane $\pi$, then $27 \cos ^2 \theta=$

$$ \lim \limits_{x \rightarrow 3} \frac{x^3-27}{x^2-9}= $$

If $f(x)=\left\{\begin{array}{ll}3 a x-2 b, & x>1 \\ a x+b+1, & x<1\end{array}\right.$ and

$\lim \limits_{x \rightarrow 1} f(x)$ exists, then the relation between $a$ and $b$ is