If the line represented by \[\frac{x-2}{2} = \frac{y-3}{3} = \frac{z-12}{5}\] passes through the point \((4,\) \(a,\) \(b)\), what is the value of \(a+b\)?

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A line \( l \) is parallel to the planes \( -4x + y = 0 \) and \( x + 5z = 0. \) Given that it passes through the point \( (4, 0, 6), \) find the equation of \( l \) in the simplest form of
\[ \frac{x-a}{p} = \frac{y-b}{q} = \frac{z-c}{r}. \]

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The following are the equations of lines that are parallel to one another:
\[ \begin{cases} \frac{x-1}{2} = \frac{y-2}{p} = \frac{z-4}{p} _,
\\\\ \frac{x-2}{q} = \frac{y-4}{2} = \frac{z-7}{3q-q^2}_,
\\\\ \frac{x}{50} = \frac{y}{11 r - 10}=\frac{z}{r^2} _.
\end{cases} \]
Find the value of \(p+q+r.\)

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The following is the equation of a line with direction vector \(\vec{d} =(p,\text{ }q,\text{ }10):\)
\[\frac{2x-u}{4}=\frac{y-2}{2} =\frac{z-2}{5}.\]
If the line passes through the point \((4,\text{ } 4,\text{ } 7),\) what is \(p+q+u\)?

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