Question 5 6 marks Paper 2 Section A Medium Calculator Free
Maximum mark: 6
The vectors \( \mathbf{a} \) and \( \mathbf{b} \) are such that
\[ \mathbf{a} = (3\cos\theta + 6)\mathbf{i} + 7\mathbf{j} \quad \text{and} \quad \mathbf{b} = (\cos\theta - 2)\mathbf{i} + (1 + \sin\theta)\mathbf{j}. \]
Given that \( \mathbf{a} \) and \( \mathbf{b} \) are perpendicular,
(a) Show that \( 3\sin^{2}\theta - 7\sin\theta + 2 = 0 \).[3]
(b) Find the smallest possible positive value of \( \theta \).[3]
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