CAIE IGCSE Mathematics E7.2 Vectors in two dimensions Question Bank

Practise writing column vectors from coordinates, combining vectors algebraically and using scalar multiples to locate points.

Exam points

[Maximum number: 3]

(a)

A is the point (3,7) and B is the point (-1,5).

[ 3 ]

(i)

Write $\overrightarrow{A B}$ as a column vector.

()

[ 1 ]

$\begin{pmatrix}-4\\-2\end{pmatrix}$

(ii)

$\overrightarrow{A C}=3 \overrightarrow{B A}$

Find the coordinates of C.

[ 2 ]

(15,13)
FT their (a)(ii)
M1 for $\begin{pmatrix}12\\6\end{pmatrix}$ or $\begin{pmatrix}-12\\-6\end{pmatrix}$ seen
or for -1+16 and 5+8 seen

[Maximum number: 2]

F is the point (1,-4), $\overrightarrow{FG}=\binom{8}{-3}$ and $\overrightarrow{GH}=\binom{-12}{35}$ .
Find

(a)

$3\overrightarrow{FG}$

[ 1 ]

$\binom{24}{-9}$

(b)

$\overrightarrow{F G}+\overrightarrow{G H}$

[ 1 ]

$\binom{-4}{32}$

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