Referred to the origin $O$, points $A$, $B$ and $C$ have position vectors $\mathbf{a}$,\(\

Question

Referred to the origin $O$, points $A$, $B$ and $C$ have position vectors $\mathbf{a}$,$\mathbf{b}$ and $\mathbf{c}$ respectively. $B$ and $C$ are points on a circle with diameter $OA$ and circumference $\pi $ units. Give a geometrical interpretation of $\left| \mathbf{a}\cdot \mathbf{b} \right|$ and show that $\mathbf{a}\cdot \mathbf{b}={{\left| \mathbf{b} \right|}^{2}}$.[3] The point $D$ is on $OA$ such that $OD:DA=4:5$. It is given that $BD$ is perpendicular to $OA$. Find the cosine of the acute angle $BOD$.[2] Given that $\left| \mathbf{a}\times \mathbf{c} \right|=0.4$, find the area of triangle $OCD$.[2]

Accepted Answer

(ii) ${\cos	heta = \frac{2}{3}}$ (iii) ${\frac{4}{45}}$

2020 NJC P2 Q2

2020 NJC P2 Q2

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