Mathematics A, Further H235: Further Vectors Topical Past Paper Questions

The line through points $ A(8,-7,-2) $ and $ B(11,-9,0) $ is denoted by $ L_{1} $. (a) Find a vector equation for $L_{1}$. [2] (b) Determine whether the point (26, -19, -14) lies on $ L_{1} $. [2] The line $L_{2}$ passes through the origin, $O$, and intersects $L_{1}$ at the poin…

The equation of line $l$ can be written in either of the following vector forms. • $ \mathbf{r} = \mathbf{a} + \lambda \mathbf{b} $, where $ \lambda \in \mathbb{R} $ • $ (\mathbf{r}-\mathbf{c}) \times \mathbf{d} = \mathbf{0} $ (a) Write down two equations involving the vectors a,…

The points $ A, B $ and $ C $ have position vectors $ \mathbf{a} = \begin{pmatrix} 3 \\ 0 \\ 0 \end{pmatrix} $, $ \mathbf{b} = \begin{pmatrix} 0 \\ 4 \\ 0 \end{pmatrix} $ and $ \mathbf{c} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} $ respectively, relative to the origin $ O $. (a…