Vectors (Chapter 11) 2913 [PQ] is the diameter of a circle with centre C.
a Find¡!
PC.
b Hence find the coordinates of Q.4 ABCD is a parallelogram.
a Find¡!
AB.
b Find¡!
CD.
c Hence find the coordinates of D.5 A(¡ 1 ,3) and B(3,k) are two points which are 5 units apart.a Find¡!
AB and j¡!
ABj.
b Hence, find the two possible values ofk.
c Show, by illustration, whykshould have two possible values.6aFind¡!
AB and¡!
AC.
b Explain why¡!
BC=¡¡!
AB+¡!
AC.
c Hence find¡!
BC.
d Check your answer tocby direct evaluation.7aGiven¡!
BA=μ
2
¡ 3¶
and¡!
BC=μ
¡ 3
1¶
, find¡!
AC.b Given¡!
AB=μ
¡ 1
3¶
and¡!
CA=μ
2
¡ 1¶
, find¡!
CB.c Given
¡!
PQ=μ
¡ 1
4¶
,
¡!
RQ=μ
2
1¶
, and
¡!
RS=μ
¡ 3
2¶
, find
¡!
SP.8aFind the coordinates of M.
b Find vectors¡!
CA,¡¡!
CM, and¡!
CB.
c Verify that
¡¡!
CM=^12
¡!
CA+^12
¡!
CB.C,(1 2)
P,(-1 1)QA,(1 4) B,(6 5)D C,(4 -1)B,(3 5)C,(4 -1)A,(1 2)MA(3 6)'B(-1 2)'
C(-4 1)'4037 Cambridge
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Y:\HAESE\CAM4037\CamAdd_11\291CamAdd_11.cdr Monday, 6 January 2014 9:56:05 AM BRIAN