3D Geometry · Distance along a line

If the distances of the point

(1, 2, a)

from the line

\dfrac{x-1}{1} = \dfrac{y}{2} = \dfrac{z-1}{1}

along the lines

L_1 : \frac{x-1}{3} = \frac{y-2}{4} = \frac{z-a}{b} \quad\text{and}\quad L_2 : \frac{x-1}{1} = \frac{y-2}{4} = \frac{z-a}{c}

are equal, then

a + b + c

is equal to

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