Mathematics: VECTORS - LINES - PLANES Topical Past Paper Questions

The plane $H_{1}$ has equation $3x - y + z = -13$ and the line $L$ has vector equation $$ \boldsymbol{r}=\begin{pmatrix}1\\2\\-2\end{pmatrix}+\lambda\begin{pmatrix}-3\\-1\\4\end{pmatrix},\lambda\in\mathbb{R}. $$ (a) Given that $L$ meets $\Pi_{1}$ at the point P, find the coordina…

[Maximum mark: 17] The points A and B have position vectors $ \begin{pmatrix} -2 \\ 4 \\ -4 \end{pmatrix} $ and $ \begin{pmatrix} 6 \\ 8 \\ 0 \end{pmatrix} $ respectively. Point C has position vector $ \begin{pmatrix} -1 \\ k \\ 0 \end{pmatrix} $. Let O be the origin. (a) Find, i…

Consider the points A(-3, 4, 2) and B(8,-1, 5). (a) (i) Find \overrightarrow{AB}. (ii) Find $ \begin{vmatrix} \overrightarrow{AB} \\ \end{vmatrix} $. [4] A line $L$ has vector equation $r = \begin{pmatrix} 2 \\ 0 \\ -5 \end{pmatrix} + t\begin{pmatrix} 1 \\ -2 \\ 2 \end{pmatrix}$.…