# 2022 HCI J2 BT Q2

##### Timothy Gan

**2022 HCI J2 BT Q2**

Relative to the origin $O$, two points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively.

It is given that $\mathbf{c}$ and $\mathbf{d}$ are vectors such that $\mathbf{c}\cdot \mathbf{d}\ne 0$.

(i)

Write down a vector equation, in scalar product form, of the plane $p$ passing through $B$ and perpendicular to $\mathbf{d}$.

[1]

(ii)

The line $l$ passes through $A$ and is parallel to $\mathbf{c}$. Let $M$ be the point of intersection of $l$ and $p$. Express $\overrightarrow{OM}$ in terms of $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$ and $\mathbf{d}$.

[3]

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