9231 P11 - Nov 2020 - Q4 - 11 marks
5804
4 The points \(A, B, C\) have position vectors
\(-\mathbf{i}+\mathbf{j}+2 \mathbf{k}, \quad-2 \mathbf{i}-\mathbf{j}, \quad 2 \mathbf{i}+2 \mathbf{k},\)
respectively, relative to the origin \(O\).
(a) Find the equation of the plane \(A B C\), giving your answer in the form \(a x+b y+c z=d\).
(b) Find the perpendicular distance from \(O\) to the plane \(A B C\).
(c) Find the acute angle between the planes \(O A B\) and \(A B C\).
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