<ol class="abc-list"><li><div class="list-item-paragraph">Given that&nbsp;$\mathbf{u}\cdot \mathbf{v}=0$, what can be deduced about the vectors $\mathbf{u}$ and $\mathbf{v}$?<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Referred to an origin $O$, the position vectors of two points $A$ and $B$ are $\mathbf{a}$ and $\mathbf{b}$ respectively. A line $~l$ has vector equation given by $\mathbf{r}=\frac{1}{3}\mathbf{a}+\lambda \left( 2\mathbf{b}-\mathbf{a} \right)$, where&nbsp;$\lambda \in \mathbb{R}$.</div><div class="list-item-paragraph">The point $N$ is the foot of perpendicular from $A$ to $l$. It is given that&nbsp;$\left| \mathbf{a} \right|=2$, $\left| \mathbf{b} \right|=1$ and $\mathbf{a}$ is perpendicular to $\mathbf{b}$.</div><ol class="i-list"><li><div class="list-item-paragraph">Find the position vector of $N$ in terms of $\mathbf{a}$ and $\mathbf{b}$.<span class="inline-marks">[5]</span></div></li><li><div class="list-item-paragraph">Find the exact area of triangle $OAN$.<span class="inline-marks">[3]</span></div></li></ol></li></ol>

Given that $\mathbf{u}\cdot \mathbf{v}=0$, what can be deduced about the vectors $\mathbf{u}$ and $\mathbf{v}$?

Referred to an origin $O$, the position vectors of two points $A$ and $B$ are $\mathbf{a}$ and $\mathbf{b}$ respectively. A line $~l$ has vector equation given by $\mathbf{r}=\frac{1}{3}\mathbf{a}+\lambda \left( 2\mathbf{b}-\mathbf{a} \right)$, where $\lambda \in \mathbb{R}$.

The point $N$ is the foot of perpendicular from $A$ to $l$. It is given that $\left| \mathbf{a} \right|=2$, $\left| \mathbf{b} \right|=1$ and $\mathbf{a}$ is perpendicular to $\mathbf{b}$.

2021 JPJC Promo Q6

2021 JPJC Promo Q6

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