Further Mathematics 7367: Further Vectors Topical Past Paper Questions

The vectors $ \mathbf{a} $, $ \mathbf{b} $, and $ \mathbf{c} $ are such that $ \mathbf{a} \times \mathbf{b} = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} $ and $ \mathbf{a} \times \mathbf{c} = \begin{bmatrix} 0 \\ 0 \\ 3 \end{bmatrix} $. Work out $ (\mathbf{a} - 4\mathbf{b} + 3\mat…

The line $l_{1}$ passes through the points $A(6,2,7)$ and $B(4,-3,7)$ (a) Find a Cartesian equation of $l_{1}$ ring a Cartesian equation or $l_{1}$ [2 marks] (b)(q) The line $ l_{2} $ has vector equation $ \mathbf{r} = \begin{bmatrix} 8 \\ 9 \\ c \end{bmatrix} + \mu \begin{bmatri…

In this question all measurements are in centimetres. A small, thin laser pen is set up with one end at $ A(7, 2, -3) $ and the other end at $ B(9, -3, -2) $ A laser beam travels from A to B and continues in a straight line towards a large thin sheet of glass. The sheet of glass…