Mathematics Pure Math 2,3 9709: VECTORS Topical Past Paper Questions

Relative to a fixed point, O, the points A, B, C and D have position vectors $$ \overrightarrow{OA}=\begin{pmatrix}2\\ 3\\ 5\end{pmatrix},\quad\overrightarrow{OB}=\begin{pmatrix}3\\ 1\\ 4\end{pmatrix},\quad\overrightarrow{OC}=\begin{pmatrix}-1\\ 0\\ -1\end{pmatrix}\quad and\quad\…

The equations of two lines are given by $$ l_1: \mathbf{r} = (2\mathbf{i} + \mathbf{j} + 4\mathbf{k}) + \lambda(\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}) $$ $$ l_2: \mathbf{r} = (3\mathbf{i} - \mathbf{j} + 5\mathbf{k}) + \mu(2\mathbf{i} + 3\mathbf{j} + a\mathbf{k}) $$ (a) Find the…

The lines $l$ and $m$ have vector equations $$ l: \mathbf{r} = 2\mathbf{i} + \mathbf{j} - 3\mathbf{k} + \lambda(-\mathbf{i} + 2\mathbf{k}) \quad \text{and} \quad m: \mathbf{r} = 2\mathbf{i} + \mathbf{j} - 3\mathbf{k} + \mu(2\mathbf{i} - \mathbf{j} + 5\mathbf{k}). $$ Lines $l$ and…