Point distance to two lines (Jee Mains)

3D Line Equations and Skew

Hard

Point distance to two lines

If the distances of the point (1, 2, a) from the line
$\frac{{x - 1}}{1} = \frac{y}{2} = \frac{{z - 1}}{1}$ along the lines
${L_1}:\frac{{x - 1}}{3} = \frac{{y - 2}}{4} = \frac{{z - a}}{b}$ and
${L_2}:\frac{{x - 1}}{1} = \frac{{y - 2}}{4} = \frac{{z - a}}{c}$ are equal,
then a + b + c is equal to

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