Referred to the origin $O$ , the position vectors of points $A$ and $B$ are \(4\mathbf{i}-11\m

Question

Referred to the origin $O$ , the position vectors of points $A$ and $B$ are $4\mathbf{i}-11\mathbf{j}+4\mathbf{k}$ and $7\mathbf{i}+\mathbf{j}+7\mathbf{k}$ respectively. Find a vector equation for the line $l$ passing through $A$ and $B$ .[2] Find the position vector of the point $P$ on $l$ such that $OP$ is perpendicular to $l$.[4]

Accepted Answer

(i) $\mathbf r=\begin{pmatrix}7 \ 1 \ 7\end{pmatrix}+\lambda\begin{pmatrix}1 \ 4 \ 1\end{pmatrix}$, $\lambda\in\mathbb R$. (ii) $\overrightarrow{OP}=\begin{pmatrix}6 \ -3 \ 6\end{pmatrix}$.

N2003 P1 Q5

N2003 P1 Q5

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