Exercise 5

Line and plane with a parameter

Theory used: Relative position of a line and a plane

As $k \in R$ varies, determine the relative position of the line $r : x = 1 + t$ , $y = 1 - t$ , $z = 2 + t$ and the plane $π_{k} : x + 2 y + k z = 4$ ; for $k = 0$ find the common point.

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