Given a line and a plane as following: Line: $x = 4 + 2t$; $y = -1 + 2t$; $z = -9 + 3t$ Plane: $3x - 6y + 2z = 7$ i) Find all intersection points of the line and the plane, if any. ii) Find the shortest distance between the line and the plane.
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Substituting the equations of the line into the equation of the plane, we have: 3(4 + 2t) - 6(-1 + 2t) + 2(9 + 3t) = 7 Simplifying the equation, we get: 12 + 6t + 6 + 12t + 18 + 6t = 7 24t + 36 = 7 24t = -29 t = -29/24 Substituting this value of t back into the Show more…
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