Mathematics 0580 · IGCSE · Vectors in two dimensions

Vectors in two dimensions — practice question

The vectors are $a = \begin{pmatrix}-3\\2\end{pmatrix}$, $b = \begin{pmatrix}5\\4\end{pmatrix}$ and $c = \begin{pmatrix}14\\9\end{pmatrix}$.
(a(i))[2]

Find the vector $3a - 2b$.

(a(ii))[2]

Find the magnitude $|a|$.

(a(iii))[5]

Write down two simultaneous equations, then solve them to obtain the values of $m$ and $n$. Show all your working.

(b(i))[5]

Find, in terms of $a$ and $c$, each expression in simplest form: (a) $\overrightarrow{AB}$, (b) $\overrightarrow{AD}$, (c) $\overrightarrow{CE}$, (d) $\overrightarrow{CD}$.

(b(ii))[1]

Find $k$.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: The answer is $(-19,-2)$.

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