Page 20 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Form
4
Chapter 8 Vectors Additional Mathematics

10. The diagram shows a triangle ABO. 13. The diagram shows a Cartesian plane where O
C3 C4 is Arif’s house, P is a shop and Q is a school.
B y
Q

C

O A
D
P
©PAN ASIA PUBLICATIONS
→ →
It is given that 2BC = 3CO, D is the midpoint
→ → →
of OA, AB = 3u and AO = 4v. Express DC in
∼
∼
terms of u and v.
∼
∼
x
–2 O 2 4 6 8 10
11. The diagram shows a parallelogram ABCD.
C3 Point Q is the intersection of the diagonals.
The shortest distance between Arif’s house and
the shop is 10 km while the shortest distance
B C between the shop and the school is 8 km.
Express the vector of Arif’s house to the school
in terms of a + b.
Q ∼ ∼
14. The points A, B and C are collinear. It is given
→
→
A D C3 that AB = 3x + 2y and BC = (1 – m)x + 4y
∼
∼
such that m is a constant, find ∼ ∼
→ →
It is given that DA = 2x + 3y and AB = 6x – y, (a) the value of m,
∼
∼
→ ∼ ∼
find CQ. (b) the ratio of AB : BC. CHAP
8
→ 15. The diagram shows a regular octagon.
12. The diagram shows OB = 8i – hj and C3
∼
→
C3 BC = 3i – 2j. ∼ F E
∼
∼
p
∼
y G D
q
∼
H C
B
r
∼
A B
C
(a) State the vectors that are equal.
→
(b) Express FA in terms of p, q and r.
∼
x ∼ ∼
O
16. A toy truck was moved at a constant velocity
C3 from point O to point P. It is given that
→
→ OP = (36i – 24j) m and the time taken is
∼
It is given |OB| = 10 units, find 6 seconds, find ∼
(a) the value of h, (a) the velocity of the toy truck,
(b) coordinates of C. (b) the speed of the toy truck.
173