EduNinja

[Maximum number: 1]

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

the coordinates of the point G

[Maximum number: 5]

(a)

The position vector of P is $\begin{pmatrix}-2\\3\end{pmatrix}$ and the position vector of Q is $\begin{pmatrix}-2\\5\end{pmatrix}$ .

[ 2 ]

(i)

R is the point such that $\overrightarrow{P R}=3 \overrightarrow{P Q}$ .

Find the position vector of R.

()

[ 2 ]

$\begin{pmatrix}-2\\9\end{pmatrix}$

FT their $\overrightarrow{PQ}$
B1FT for $\begin{pmatrix}0\\6\end{pmatrix}$

(b)

Figure for Question (b) — CAIE IGCSE Mathematics Extended

$\overrightarrow{O T}=\mathbf{t}, \overrightarrow{O U}=\mathbf{u}$ and U Y=2 Y T.

[ 3 ]

(i)

Find $\overrightarrow{O Y}$ in terms of t and u.

Give your answer in its simplest form.

\overrightarrow{O Y}=

[ 2 ]

$\overrightarrow{OY}=\frac{2}{3}\mathbf{t}+\frac{1}{3}\mathbf{u}=\frac{1}{3}(2\mathbf{t}+\mathbf{u})$

M1 for $\overrightarrow{UY}=\frac{2}{3}(\mathbf{t}-\mathbf{u})$ oe or $\overrightarrow{TY}=\frac{1}{3}(\mathbf{u}-\mathbf{t})$ oe or correct route soi

(ii)

$\quad Z$ is on OT and YZ is parallel to UO.

Find $\overrightarrow{O Z}$ in terms of t and/or u.
Give your answer in its simplest form.

\overrightarrow{O Z}=

[ 1 ]

$\overrightarrow{OZ}=\frac{2}{3}\mathbf{t}$
cao

CAIE IGCSE Mathematics Extended E7.4 Vector Geometry Topic Practice

Question 1

Question 2

Question (a)

Question (i)

Question (b)

Question (i)

Question (ii)