Vectors (Cambridge International IGCSE Maths): Exam Questions

$A$ is the point $( 1 , 2 )$ and $\vec{AB} = ( - 1 3 )$.

Find the coordinates of the point $B$.

Work out $2 ( 2 3 ) - ( - 3 5 )$.

$( )$

Ahmed finds the magnitude of the vector $( 2

• 3 )$. From this list, select the correct calculation.

$\sqrt{2^{2} + - 3^{2}} 2^{2 } - 3^{2} \sqrt{2^{2} - 3^{2}} 2^{2 } + ( - 3^{2} ) \sqrt{2^{2} + ( - 3 )^{2}}$

$m = ( \begin{gathered} 5 \\ 7 \end{gathered} )$ Find $3m$.

$( \begin{gathered} \\ \end{gathered} )$

Find the magnitude of the vector $( \begin{gathered} - 1 \\ 7 \end{gathered} )$.

i) Find the column vector $\overset{\rightarrow}{AB}$.

$\vec{AB} = ( \begin{gathered} \\ \end{gathered} )$ [1]

ii) Find $\vert \vec{AB} \vert$.

$\vert \vec{AB} \vert =$................................................. [2]

Find the magnitude of the vector $( - 6 8 )$ .

$\vec{VW} = ( \begin{gathered} 10 \\ - 24 \end{gathered} )$ Find $\left| \vec{VW} \right| .$

$u = ( \begin{gathered} 3 \\ - 2 \end{gathered} ) v = ( \begin{gathered} - 12 \\ 5 \end{gathered} )$

Find $u--2v.$

Extract:

$v = \left(\begin{pmatrix} - 12 \\ 5\end{pmatrix}\right)$

Find $\left| v\right|$ .

$p = ( \begin{gathered} 4 \\ 5 \end{gathered} )$ $q = ( \begin{gathered} - 2 \\ 7 \end{gathered} )$

i) Find $2p+q.$

$( \begin{gathered} \\ \end{gathered} )$ [2]

ii) Find $\left| p \right|$.

$m = ( \begin{gathered} 5 \\ 7 \end{gathered} )$ Find $3m$.

$( \begin{gathered} \\ \end{gathered} )$

$a = ( \begin{gathered} - 3 \\ 2 \end{gathered} ) b = ( \begin{gathered} 5 \\ 4 \end{gathered} ) c = ( \begin{gathered} 14 \\ 9 \end{gathered} )$

i) Find $3a-2b$ .

$( \begin{gathered} \\ \end{gathered} )$ [2]

ii) Find $\vert a \vert$.

$A$ is the point (-2, 1) and $\vec{AB} = ( \begin{gathered} 4 \\ 2 \end{gathered} )$.

Find the coordinates of point $B$.

$p = ( 3

• 2 ) q = ( - 5 1 )$

(i) Work out $p+2q$.

(ii) $A$is the point $( 2 , 6 )$ and $B$ is the image of point $A$after a translation by the vector $p$.

Find the coordinates of $B$.

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

(iii) Find the magnitude of $q$.

$a = ( \begin{gathered} - 3 \\ 2 \end{gathered} ) b = ( \begin{gathered} 5 \\ 4 \end{gathered} ) c = ( \begin{gathered} 14 \\ 9 \end{gathered} )$

$ma+nb=\text{c}$

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

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

$\vec{MT} = ( 2 k

• k )$and$\left| \vec{MT} \right| = \sqrt{180}$. Find the positive value of$k$.

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