9709 P13 - Jun 2015 - Q5
2191
Relative to an origin O, the position vectors of the points A, B and C are given by
\(\overrightarrow{OA} = \begin{pmatrix} 3 \\ 2 \\ -3 \end{pmatrix}, \quad \overrightarrow{OB} = \begin{pmatrix} 5 \\ -1 \\ -2 \end{pmatrix} \quad \text{and} \quad \overrightarrow{OC} = \begin{pmatrix} 6 \\ 1 \\ 2 \end{pmatrix}.\)
(i) Show that angle \(ABC\) is \(90^\circ\).
(ii) Find the area of triangle \(ABC\), giving your answer correct to 1 decimal place.
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