Page 294 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

EXAMPLE 10
In a regular pentagon ABCDE, AB = p, BC = q and CD = r. Determine:
(c)
(a) AC (a)
(b) AD
(c) BD B
D
BD = BC + CD BD = q + r
So
AC = p + q B
(a) AC
(b) BD R
Q
P
2. C
r
D E
A
B
q
C
r
E
Consider triangle BCD and use the triangle law of vectors:
A
E
p +q
C
So
Consider triangle ABC and use the triangle law of vectors: AC = AB + BC
1.
D
EXERCISE 13.10
ABCD is a rhombus with AB = a and BC = b. Evaluate :
(b)
A
p C
Consider the quadrilateral ABCD and use the polygon law of vectors:
PQRS is a kite with PQ = k and QR = l. Determine:
(a) PR (b) RP
AD = AB + BC + CD So AD = p + q + r
3.
ab
KcL
S
N
M
KLMN is a trapezium with KN = 9, LM = B and KL = c. Determine:
(a) NM (b) LM (c) MK 288
q +r
p + q 4r