Further Pure Mathematics WFM01: VECTORS Topical Past Paper Questions

Figure 1 The points $A, B$ and $C$ have position vectors $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ respectively, relative to a fixed origin $O$, as shown in Figure 1, where $$ \mathbf{a}=2\mathbf{i}-\mathbf{k}\quad\mathbf{b}=\mathbf{i}+2\mathbf{j}-2\mathbf{k}\quad\mathrm{a n d}\q…

The plane $ II_{1} $ has equation $$ \mathbf{r}=\left(\begin{matrix}{4}\\ {2}\\ {-1}\\ \end{matrix}\right)+\lambda\left(\begin{matrix}{7}\\ {5}\\ {-6}\\ \end{matrix}\right)+\mu\left(\begin{matrix}{-3}\\ {1}\\ {2}\\ \end{matrix}\right) $$ where $\lambda$ and $\mu$ are scalar param…

The plane $H_{1}$ has vector equation $$ \mathbf{r}=\left(\begin{matrix}{5}\\ {3}\\ {0}\\ \end{matrix}\right)+s\left(\begin{matrix}{3}\\ {0}\\ {1}\\ \end{matrix}\right)+t\left(\begin{matrix}{1}\\ {-2}\\ {2}\\ \end{matrix}\right) $$ where s and t are scalar parameters. (a) Determi…