Line Distance Sum (Jee Mains)

3D Line Equations and Skew

Medium

Line Distance Sum

Let L be the line $\frac{{x + 1}}{2}$ = $\frac{{y + 1}}{3}$ = $\frac{{z + 3}}{6}$ and let S be the set of all points (a, b, c) on L, whose distance from the line $\frac{{x + 1}}{2} = \frac{{y + 1}}{3} = \frac{{z - 9}}{0}$ along the line L is 7. Then $\sum\limits_{(a,b,c)\; \in \;S} {(a + b + c)}$ is equal to :

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