CAIE IGCSE Mathematics Extended E7.4 Vector Geometry Topic Practice

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Covered syllabus points

E7.4.1 Represent vectors by directed line segments.E7.4.2 Use position vectors.E7.4.3 Use the sum and difference of two or more vectors to express givenE7.4.4 Use vectors to reason and to solve geometric problems

Question 1

[Maximum number: 1]

F is the point (1,-4), FG→=(8−3)\overrightarrow{FG}=\binom{8}{-3} and GH→=(−1235)\overrightarrow{GH}=\binom{-12}{35}.
Find

the coordinates of the point G

Question 2

[Maximum number: 1]
Figure for Question 2 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

The diagram shows a triangle OAC. A is the midpoint of the straight line OB. OA→=x\overrightarrow{OA}=\mathbf{x} and OC→=y\overrightarrow{OC}=\mathbf{y}.
Find CB→\overrightarrow{CB} in terms of x\mathbf{x} and y\mathbf{y}.
CB→=\overrightarrow{CB}=

Question 3

[Maximum number: 6]

The diagram shows triangle OPT.

Figure for Question 3 — CAIE IGCSE Mathematics Extended

NOT TO
SCALE

In the diagram OT→=t\overrightarrow{O T}=\mathbf{t} and OP→=p\overrightarrow{O P}=\mathbf{p}.
O K: K T=2: 1 and T L: L P=2: 1.

Question (a)

(a)

Find, in terms of t and p, in its simplest form

[ 4 ]

Question (i)

(i)

PL→\overrightarrow{P L}

[ 2 ]

Question (ii)

(ii)

KL→\overrightarrow{K L}.

[ 2 ]

Question (b)

(b)

KL is extended to the point M.
KM→=−23t+43p\overrightarrow{K M}=-\frac{2}{3} \mathbf{t}+\frac{4}{3} \mathbf{p}.

Show that M lies on OP extended.

[ 2 ]
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