Shortest distance between two lines (Jee Mains)

3D Line Equations and Skew

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Shortest distance between two lines

Let P(α, β, γ) be the point on the line $\frac{{x - 1}}{2} = \frac{{y + 1}}{{ - 3}} = z$ at a distance $4\sqrt {14}$ from the point (1, –1, 0) and nearer to the origin. Then the shortest distance, between the lines $\frac{{x - \alpha }}{1} = \frac{{y - \beta }}{2} = \frac{{z - \gamma }}{3}$ and $\frac{{x + 5}}{2} = \frac{{y - 10}}{1} = \frac{{z - 3}}{1}$ , is equal to

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