AS June 2021 Paper 1 Q3

3 The matrix \(\mathbf{M}\) represents a rotation about the \(x\)-axis.

\[\mathbf{M} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & a & \dfrac{\sqrt{3}}{2} \\ 0 & b & -\dfrac{1}{2} \end{bmatrix}\]

Which of the following pairs of values is correct?

Tick (✓) one box. [1 mark]

• \(a = \dfrac{1}{2}\) and \(b = \dfrac{\sqrt{3}}{2}\)
• \(a = \dfrac{1}{2}\) and \(b = -\dfrac{\sqrt{3}}{2}\)
• \(a = -\dfrac{1}{2}\) and \(b = \dfrac{\sqrt{3}}{2}\)
• \(a = -\dfrac{1}{2}\) and \(b = -\dfrac{\sqrt{3}}{2}\)