- \(\left[ \begin{array} { l } \text { With respect to the right-hand rule, a rotation through } \theta ^ { \circ } \text { anticlockwise about the }
y \text {-axis is represented by the matrix } \end{array} \right]\)
\(\left( \begin{array} { c c c } \cos \theta & 0 & \sin \theta
0 & 1 & 0
- \sin \theta & 0 & \cos \theta \end{array} \right)\)
The point \(P\) has coordinates (8, 3, 2)
The point \(Q\) is the image of \(P\) under the transformation reflection in the plane \(y = 0\)
- Write down the coordinates of \(Q\)
The point \(R\) is the image of \(P\) under the transformation rotation through \(120 ^ { \circ }\) anticlockwise about the \(y\)-axis, with respect to the right-hand rule.
- Determine the exact coordinates of \(R\)
- Hence find \(| \overrightarrow { P R } |\) giving your answer as a simplified surd.
- Show that \(\overrightarrow { P R }\) and \(\overrightarrow { P Q }\) are perpendicular.
- Hence determine the exact area of triangle \(P Q R\), giving your answer as a surd in simplest form.