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

Question

Referred to the origin $O$, the points $A$ and $B$ have position vectors $\mathbf a$ and $\mathbf b$ respectively. It is given that $|\mathbf a|=\sqrt2|\mathbf b|$ and $\mathbf a$ is perpendicular to $\mathbf b$. The point $P$ lies on $AB$ such that $AP:PB=2:1$. Show that $OP$ is perpendicular to $AB$.[3] It is now given that $|\mathbf b|=2$. Find the exact length of $OP$.[3]

Accepted Answer

(a) $\overrightarrow{OP}\cdot\overrightarrow{AB}=0$. (b) $\dfrac{2\sqrt6}{3}$.

2026 CJC Promo Q3

2026 CJC Promo Q3

Solution:

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