## Question

###### [Maximum mark: 15]Consider a triangle OAB such that 0 has coordinates (0 0 ,0),A has coordinates (0 1,2) and B has coordinates (2b , 0 b _ 1) where b < 0 _(a) Find, in terms of b, a Cartesian equation of the plane II containing this triangle.Let M be the midpoint of the line segment [OB] -(b) Find, in terms of b , the equation of the line L which passes through M and is perpendicular to the plane II.(c) Show that L does not intersect the Y-axis for any negative value of b _

[Maximum mark: 15] Consider a triangle OAB such that 0 has coordinates (0 0 ,0),A has coordinates (0 1,2) and B has coordinates (2b , 0 b _ 1) where b < 0 _ (a) Find, in terms of b, a Cartesian equation of the plane II containing this triangle. Let M be the midpoint of the line segment [OB] - (b) Find, in terms of b , the equation of the line L which passes through M and is perpendicular to the plane II. (c) Show that L does not intersect the Y-axis for any negative value of b _

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