Moderate -0.8 This is a straightforward application of standard vector methods: compute two vectors in the plane (AB and AC), verify perpendicularity using dot products (which should yield zero), then write the plane equation using the given normal vector and a point. All steps are routine C4 techniques with no problem-solving insight required, making it easier than average but not trivial due to the computational work involved.
Verify that the vector \(2\mathbf{i} - \mathbf{j} + 4\mathbf{k}\) is perpendicular to the plane through the points A(2, 0, 1), B(1, 2, 2) and C(0, -4, 1). Hence find the cartesian equation of the plane. [5]
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Verify that the vector $2\mathbf{i} - \mathbf{j} + 4\mathbf{k}$ is perpendicular to the plane through the points A(2, 0, 1), B(1, 2, 2) and C(0, -4, 1). Hence find the cartesian equation of the plane. [5]
\hfill \mbox{\textit{OCR MEI C4 2012 Q5 [5]}}