Further Pure Math 9-1 4PM1: Scalar and vector quantities Topical Past Paper Questions

The points $A, B, C$ and $D$ are the vertices of a quadrilateral where $$ \overrightarrow{AB}=2\mathbf{a}+4\mathbf{b}\qquad\overrightarrow{AC}=7\mathbf{a}+7\mathbf{b}\qquad\overrightarrow{AD}=10\mathbf{a}+6\mathbf{b} $$ (a) Show that ABCD is a trapezium. (4) Given that $ |\mathbf…

Diagram NOT accurately drawn Figure 2 Figure 2 shows triangle AOB $$ \overrightarrow{OA}=4\mathbf{a}+5\mathbf{b}\qquad\overrightarrow{OB}=8\mathbf{a}-\mathbf{b}\qquad\overrightarrow{OD}=15\mathbf{a}+10\mathbf{b}\qquad\text{where}|\mathbf{a}|=|\mathbf{b}|=1 $$ (a) (i) Find $ \over…

O, A and B are fixed points such that $$ \overrightarrow{O A}=5\mathbf{i}+7\mathbf{j}\qquad\overrightarrow{A B}=a\mathbf{i}+16\mathbf{j}\qquad\mathrm{a n d}\qquad\left|\overrightarrow{O B}\right|=5\sqrt{29} $$ (a) Find the possible values of $a$ (4) Given that $a > 0$ (b) find a…