Vectors - Perpendicular Vectors Using the Scalar Product
Vectors - Perpendicular Vectors Using the Scalar Product
The diagram below shows a circle with centre \(O\). The points \(A\), \(B\), and \(C\) lie on the circumference of the circle and \(AC\) is a diameter.
Let \(\overrightarrow{OA}=\mathbf{a}\) and \(\overrightarrow{OB}=\mathbf{b}\).
- Write down expressions for \(\overrightarrow{AB}\) and \(\overrightarrow{CB}\) in terms of the vectors \(\mathbf{a}\) and \(\mathbf{b}\).
- Hence prove that angle \(ABC\) is a right angle.
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Answer:(a) \(\overrightarrow{AB}=\mathbf{b}-\mathbf{a}\), \(\overrightarrow{CB}=\mathbf{a}+\mathbf{b}\)
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