Given 2p − 3q + r = 0, p = 2i − 7j, and q = -5i - 9j, find the magnitude of vector r.

Given the equation $2p - 3q + r = 0$, we can solve for $r$:

$$r = -2p + 3q$$

Given $p = 2i - 7j$ and $q = -5i - 9j$.

$$r = -2(2i - 7j) + 3(-5i - 9j)$$

First, multiply the scalars into the vectors:

$$-2(2i - 7j) = -4i + 14j$$ $$3(-5i - 9j) = -15i - 27j$$

Now, add these two resulting vectors:

$$r = (-4i + 14j) + (-15i - 27j)$$

Combine the $i$ components and the $j$ components:

$$r = (-4 - 15)i + (14 - 27)j$$ $$r = -19i - 13j$$

For a vector $r = xi + yj$, its magnitude is given by $|r| = \sqrt{x^2 + y^2}$.
Here, $x = -19$ and $y = -13$.

$$|r| = \sqrt{(-19)^2 + (-13)^2}$$ $$|r| = \sqrt{361 + 169}$$ $$|r| = \sqrt{530}$$

The final answer is $\mathbf{\sqrt{530}}$.