SPM Add Math Form 5 Chapter 4 Vector
CHAPTER 4 : VECTOR
1) Based on the diagram below, state the vectors which are equal to the given vectors.
(a) b =
(b) c =
(c) e =
(d) i =
(e) k =
2) Construct the following vectors on the square grid below.
(a) 2a
(b) 3a
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(c)
a
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SPM Add Math Form 5 Chapter 4 Vector
3) Based on the diagram below, find the value of k in each case, where k is a constant.
(a) s = kr
(b) r = kp
(c) p = ks
(d) p = kt
(e) q = kt
4) Based on the diagram below, determine the vectors that are parallel. Then, state their
relationships.
(a)
and ________are parallel vectors.
= _________
(b)
and ________are parallel vectors.
= _________
(c)
and ________are parallel vectors.
= _________
(d)
and ________are parallel vectors.
= _________
(e)
and ________are parallel vectors.
= _________
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SPM Add Math Form 5 Chapter 4 Vector
5) Determine the resultant vector of each of the following.
(a)
p + 2q + 3p + q
(b) 2a + 3b + a + b
6) Solve each of the following. Given that
(a)
a and
a.
(b)
7) Determine the resultant vector of each of the following.
(a) ABCDE is a pentagon.
(i) a + b =
(ii) c + d =
(iii)
(b) KLMN is a parallelogram.
(i)
(ii)
(iii)
=
(iv)
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SPM Add Math Form 5 Chapter 4 Vector
8) Express each vector below in terms of a and b.
(a) In triangle OAB, M is the midpoint of OB. Given that
and
a
b, find
(i)
(ii)
(b) In triangle OAB, M is the midpoint of AB and P lies on OM such that
Given that
a and
.
b, find
(i)
(ii)
(iii)
9) In the diagram, ABCD is a parallelogram. Given
such that
= 12a and
= 9b. M lies on AD
.
(a) Express each of the following vectors, in terms of a and b.
(i)
(ii)
(b) If
and
(i) k, a and b
10) In the diagram,
positions such that
and
(iii)
express
(ii) m, a and b
in terms of
represent vector 2a and 2b. Points C and D are in the
a + 2b and
(a) Prove by vector method that
= 2a + b.
is parallel to
(b) OD and AB intersect at E. If
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and
, then find the ratio of CD : BA .
find the value of h and of k.
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SPM Add Math Form 5 Chapter 4 Vector
11) In the diagram,
= 12b and
= 4c,
and
(a) Express the vectors below, in terms of b and c.
(i)
(ii)
(iii)
(b) Given that
and
the value of h and of k.
By applying the triangle law on triangle ADE, find
(c) If the area of triangle ABC = 60cm2, find the area, in cm2, of triangle ACD.
12) Determine
for each of the following.
(b) a = 12i – 5j
(a) a = 4i +3j
13) Given that a = 2i, b = 3i – 5j and c = -i + 4j , find each of the following.
(a) a + 2b – 3c
(b) 2a + b – 3c
14) Given that p =
q=
(a) 2p – q + 3r
15) Given that
16) Given
, determine each of the following.
and r =
(b) p + 2q - r
= 2i + 4j,
= 2i + 2j,
= -3i + kj and
= 4i + 3j and
is parallel to
, find the value of k.
= 6i + 4j .
(a) Find
(i)
,
(ii)
(b) Hence, prove that P, Q and R lie on a straight line.
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SPM Add Math Form 5 Chapter 4 Vector
17) In the diagram given, ABCD is a rectangle with
= 12i ,
= 8j . Given that
=
.
(a) Find vectors
,
and
in terms of i and j.
(b) Find the length, in cm, of the perpendicular distance from A to BD, given the area of
triangle ABD = 48 cm2 and
=
= 1 cm.
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