Maths Core WMA01/WMA02: VECTORS Topical Past Paper Questions

With respect to a fixed origin $O$, the lines $l_{1}$ and $l_{2}$ are given by the equations $$ l_{1}:\quad\mathbf{r}=\begin{pmatrix}2\\ 1\\ 3\end{pmatrix}+\lambda\begin{pmatrix}-2\\ 1\\ 4\end{pmatrix} $$ $$ l_{2}:\quad\mathrm{r}=\begin{pmatrix}10\\ c\\ 3\end{pmatrix}+\mu\begin{p…

Relative to a fixed origin O, the point A has position vector $ (2\mathbf{i} - 3\mathbf{j} - 2\mathbf{k}) $ the point B has position vector $ (3\mathbf{i} + 2\mathbf{j} + 5\mathbf{k}) $ the point C has position vector $ (2\mathbf{i} + 4\mathbf{j} - 3\mathbf{k}) $ The line $l$ pas…

With respect to a fixed origin O, the lines $ l_{1} $ and $ l_{2} $ are given by the equations $$ l_{1}:\mathbf{r}=(13\mathbf{i}+15\mathbf{j}-8\mathbf{k})+\lambda(3\mathbf{i}+3\mathbf{j}-4\mathbf{k}) $$ $$ l_{2}:\mathbf{r}=(7\mathbf{i}-6\mathbf{j}+14\mathbf{k})+\mu(2\mathbf{i}-3\…