In the diagram below, $AB$ is a diameter of the circle with centre $O$. Point $C$ is on the ci

Question

In the diagram below, $AB$ is a diameter of the circle with centre $O$. Point $C$ is on the circumference of the circle. Let $\overrightarrow{OB}=\mathbf{b}$ and $\overrightarrow{OC}=\mathbf{c}$. Find an expression for $\overrightarrow{CB}$ and for $\overrightarrow{AC}$ in terms of $\mathbf{b}$ and $\mathbf{c}$. Hence prove that $ACB$ is a right angle.

Accepted Answer

(a) $\overrightarrow{CB}=\mathbf b-\mathbf c$, $\overrightarrow{AC}=\mathbf b+\mathbf c$ (b) $\angle ACB=90^\circ$

Vectors - Perpendicular Vectors Using the Scalar Product

Vectors - Perpendicular Vectors Using the Scalar Product

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