Vectors (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

Find the magnitude of the vector $$\begin{gathered} \left(-6 \\ 8\right) \end{gathered}$$ .

$\overrightarrow{VW}=\left(\begin{array}{c}10\\ -24\end{array}\right)$
Find  $\left|\overrightarrow{VW}\right|.$

$\mathbf{u}=\left(\begin{array}{c}3\\ -2\end{array}\right)\mathit{v}=\left(\begin{array}{c}-12\\ 5\end{array}\right)$

Find $\mathbf{u}–2\mathbf{v}.$

Find $\left|\mathbf{v}\right|$ .

$\mathbf{p}=\left(\begin{array}{c}4\\ 5\end{array}\right)$       $\mathbf{q}=\left(\begin{array}{r}-2\\ 7\end{array}\right)$

i) Find $2\mathbf{p}+\mathbf{q}.$  

$\left(\begin{array}{c}\\ \end{array}\right)$ [2]

ii) Find $\left|\mathbf{p}\right|$.  

[2]

$\mathbf{m}=\left(\begin{array}{c}5\\ 7\end{array}\right)$
Find $3\mathbf{m}$.

$\left(\begin{array}{c}\\ \end{array}\right)$  

$\mathbf{a}=\left(\begin{array}{c}-3\\ 2\end{array}\right)\mathbf{b}=\left(\begin{array}{c}5\\ 4\end{array}\right)\mathbf{c}=\left(\begin{array}{c}14\\ 9\end{array}\right)$

i) Find  $3\mathbf{a}-2\mathbf{b}$ .

 $\left(\begin{array}{c}\\ \end{array}\right)$ [2]

ii) Find  $\left|\mathbf{a}\right|$.

[2]

$A$ is the point (-2, 1) and $\overrightarrow{AB}=\left(\begin{array}{c}4\\ 2\end{array}\right)$.

Find the coordinates of point $B$.

$$\begin{gathered} \mathbf{p}=\left(3 \\ -2\right)\mathbf{q}=\left(-5 \\ 1\right) \end{gathered}$$

(i) Work out $\mathbf{p}+2\mathbf{q}$.

[2]

(ii) $A$is the point $\left(2,6\right)$ and $B$ is the image of point $A$after a translation by the vector $\mathbf{p}$.

Find the coordinates of $B$.

( ...................... , ...................... ) [1]

(iii) Find the magnitude of $\mathbf{q}$.

[2]

$\mathbf{a}=\left(\begin{array}{c}-3\\ 2\end{array}\right)\mathbf{b}=\left(\begin{array}{c}5\\ 4\end{array}\right)\mathbf{c}=\left(\begin{array}{c}14\\ 9\end{array}\right)$

$m\mathbf{a}+n\mathbf{b}=\mathbf{\text{c}}$  

Write down two simultaneous equations and solve them to find the value of $m$ and the value of $n$. Show all your working.  

$m$ = ................................................     
$n$ = ................................................      

$$\begin{gathered} \overrightarrow{MT}=\left(2k \\ -k\right) \end{gathered}$$  and  $\left|\overrightarrow{MT}\right|=\sqrt{180}$.  
Find the positive value of $k$.

$k=$ ..............................................