Page 21 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Form
4 Additional Mathematics Chapter 8 Vectors

→
→
→
SPM Clone
SPM Clone
17. The diagram shows a regular decagon with 20. The diagram shows vectors AC , AB and AD
center O. drawn on a square grid with sides of 1 unit.
C3 C3
G F
A
H E
D
I O D
C
B
G C
A B
→ → → → → →
(a) Express BC + CH + HJ + FE as a single (a) It is given that AB = p and AC = q,
∼
∼
→
vector. express AD in terms of mp + nq, where m
→ → ∼ ∼
(b) It is given OE = x, OD = y and the length and n are constants.
∼
∼
of each side of the decagon is 2 units. Find (b) On the diagram above, mark and label
→ → → →
the unit vector in the direction of ED , in point E such that DE + AC = 3AB.
terms of x and y.
∼
∼
21. A school bus depart from Kampung Merbau
→
→
→
SPM Clone
18. The diagram shows vectors QP , QS and QR C4 with a position vector (40i + 30j) km to
∼
∼
SMK Saujana Utama with a position vector
C3 drawn on a square grid with sides of 1 unit. (25i + 16j) km. The school bus travels with
∼
∼
constant velocity and take 1 hour back and
forth to take and drop off students. Find the
Q velocity of the vector.
R
–6
7
∼    
CHAP ©PAN ASIA PUBLICATIONS
22. The equation u =
+ t
represents the
S
8 C4 5 8
P path of a moving particle where t is in seconds
and the distance is in meter. Find
→
(a) Find |– PQ |. (a) the initial position of the particle,
→ → (b) the velocity of the particle,
(b) It is given that QP = x and QS = y,
∼
express in terms of x and y, ∼ (c) the speed of the particle.
→ ∼ ∼ →
(i) PS (ii) QR .
23. In an archery competition, an arrow hits
C4 3 points on archery’s board. The points have
SPM Clone
19. It is given that K(2, m), L(n, 7), p = 7i + 4j, position vectors that marked E, F and G are
∼
∼
∼
→
∼
∼
C3 q = –i – 8j and KL = p – hq where m, n and h ∼ i – j, 5i – 3j and 11i – 6j. Show that E, F and
∼
∼
∼
∼
∼
∼
∼
∼
are constants, express n in terms of m. G are collinear.
174