Angle between two intersecting linesHard

Foot of Perpendicular and Line Intersection

Let P be the foot of the perpendicular from the point (1, 2, 2) on the line L : $\frac{{x - 1}}{1} = \frac{{y + 1}}{{ - 1}} = \frac{{z - 2}}{2}$ . Let the line $\vec r = \left( { - \hat i + \hat j - 2\hat k} \right) + \lambda \left( {\hat i - \hat j + \hat k} \right)$ , λ ∈ R, intersect the line L at Q. Then 2(PQ)² is equal to:

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