Mathematics A H230: Vectors Topical Past Paper Questions

A particle $P$ of mass 2.5 kg is in equilibrium under the action of three horizontal forces $\mathbf{F}_{1} = \begin{pmatrix} 3 \\ -7 \end{pmatrix} \mathbf{N}$, $\mathbf{F}_{2} = \begin{pmatrix} -5 \\ 10 \end{pmatrix} \mathbf{N}$ and $\mathbf{F}_{3}$. (a) Find the force $\mathbf{…

(a) (i) Show that (ii) Find the ratio AB : BC. (b) The diagram shows the line $ x+y=6 $ and the point $ P(2,4) $ that lies on the line. A copy of the diagram is given in the Printed Answer Booklet. The distinct point Q also lies on the line $ x+y=6 $ and is such that $ \left|\ove…

(a) Simplify $ 2\binom{6}{-3} - 3\binom{-1}{2} $. [2] (b) The vector $ \mathbf{a} $ is defined by $ \mathbf{a} = r\binom{6}{-3} + s\binom{-1}{2} $, where $ r $ and $ s $ are constants. Determine two pairs of values of $ r $ and $ s $ such that $ \mathbf{a} $ is parallel to the $…