A2 June 2019 Paper 1 Q2

OCR MEICurrent spec3 marks3D Lines & Planes

2 The plane \(x + 2y + cz = 4\) is perpendicular to the plane \(2x - cy + 6z = 9\), where \(c\) is a constant. Find the value of \(c\). [3]

Mark scheme

Scheme	Marks	AO
\((\mathbf{i} + 2\mathbf{j} + c\mathbf{k}).(2\mathbf{i} - c\mathbf{j} + 6\mathbf{k}) = 0\)	M1	1.1a
\(\Rightarrow 2 - 2c + 6c = 0\)	A1	1.1b
\(\Rightarrow c = -\frac{1}{2}\)	A1	1.1b
	[3]

M1: scalar product = 0