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

Question

Given that $\mathbf{u}\cdot \mathbf{v}=0$, what can be deduced about the vectors $\mathbf{u}$ and $\mathbf{v}$?[2] 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 $\mathbf{b}$. Find the position vector of $N$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[5] Find the exact area of triangle $OAN$.[3]

Accepted Answer

(a) $\mathbf u=\mathbf0$, or $\mathbf v=\mathbf0$, or the two non-zero vectors are perpendicular. (b)(i) $\overrightarrow{ON}=\frac23\mathbf a-\frac23\mathbf b$. (b)(ii) $\frac23\text{ units}^2$.

2021 JPJC Promo Q6

2021 JPJC Promo Q6

Video Solution:

Solution:

Solution locked