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Exam-Style Questions on VectorsProblems on Vectors adapted from questions set in previous GCSE Extended exams. |
1. | IGCSE Extended |
OABC is a parallelogram with O as origin. The position vector of A is \(a\) and the position vector of C is \(c\).
F is the mid-point of AB and the point E divides the line OC such that OE:EC = 2:1.
The point E also divides the line AD such that AE:ED = 3:2.
Find the following in terms of \(a\) and \(c\).
(a) \(\overrightarrow{OB}\)
(b) \(\overrightarrow{AC}\)
(c) \(\overrightarrow{AE}\)
(d) the position vector of F.
(e) \(\overrightarrow{AD}\)
(f) \(\overrightarrow{BD}\)
2. | IGCSE Extended |
ABCDOE is a regular hexagon with O as origin. The position vector of A is \(a\) and the position vector of B is \(b\).
Find the following in terms of \(a\) and \(b\).
(a) \(\overrightarrow{BA}\)
(b) \(\overrightarrow{OE}\)
(c) the position vector of C.
If the sides of the hexagon are each of length 10cm calculate:
(d) the size of angle \(BCD\).
(e) the area of triangle \(BCD\).
(f) the length of the line from B to D.
(g) the area of the hexagon.
3. | IGCSE Extended |
(a) If A is the point (3,5) write down the position vector of A.
(b) If B is the point (6,9) find \(\mid\overrightarrow{AB} \mid\) the magnitude of \( \overrightarrow{AB}\).
The following diagram is not to scale.
\(O\) is the origin, \(\overrightarrow{OP}=p\) and = \(\overrightarrow{OQ}=q\).
\(OP\) is extended to \(R\) so that \(OP=PR\).
\(OQ\) is extended to \(S\) so that \(OQ=QS\).
(c) Write down \(\overrightarrow{RQ}\) in terms of \(p\) and \(q\).
(d) \(PS\) and \(RQ\) intersect at \(M\) and \(RM=2 MQ\).
Use vectors to find the ratio \(PM:PS\), showing all your working.
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