Page 58 - ACE YR IGCSE A TOP APPR' TO ADD MATH

→ → →
12 Vectors 6. AB = AO + OB
7
–10
+
= 1 2 1 2
→ –4 –12
2
2
1. (a) |AB| = √(–4) + (3) –3
–16
= √25 = 1 2
= 5 → –3
[1] AC = 3 1 2
–16
(b) 1 (–4i + 3j)
–9
5 [1] = 1 2
–48
→
→
→
2. |p – q + r| OC = OA + AC
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4
3
2
u
1
2
u
= 3i – (–2i) – i + 5j – – i + 14 j = 1 2 1 2
–7
–9
+
3
7
4
u
= u 13 i + 81 j = 1 2 –48
–16
14
3
–44
13
81
2
= 1 2 1 2 2 |OC| = √(–16) + (–44)
+
→
14
3
2
2
= 7.23 = 4√137
[3] [4]
→
2 →
1
u
u
3. 2c – a + b 7. BC = (AC)
5
5
→
2 →
→
→
4
1
7
2 1
u 1
u
= 2 – i + j – –3i + 5j 2 + (–6j) BO + OC = (AO + OC)
5
5
3
2
5
2
5
6
3
8
u
u
= – 14 i + i + j – j – j –µ(–2i + j) + l(–3i – 8j) = [−(4i − 5j) + l(−3i − 8j)]
5
5
2
3
5
2
8
6
2µ – 3l = – – l
5
5
u
u
= – 19 i + 21 j 10µ – 15l = –8 – 6l
6
10
2
21
1
= – 19 2 1 2 2 10µ = 9l – 8
+
9l – 8
10
6
µ =
= 3.8 10 16
[3] –µ – 8l = –2 – l
5
4. a(–3i + 5j) + 10j = b(6i) µ = –8l + 16 l + 2
–3a = 6b 5
a = –2b µ = – 24 l + 2
5
5a + 10 = 0 9l – 8 –24l + 10
5(–2b) + 10 = 0 10 = 5
b = 1 9l – 8 = –48l + 20
a = –2
[3] 57l = 28
→ → → l = 28
5. (a) AB = AO + OB 57
= 3i – 7j + 6i – j 24 28
1 2
= 9i – 8j µ = – 5 57 + 2
[2] 34
1 → → = –
(b) AB = CB 95
3 [7]
1 → → →
AB = CO + OB −3 × 5 + 13 × 3
3 8. (a) d =
→ → 1 → 8
OC = OB – AB = 3
3 e × 5 – 20 × 3
1
= 6i – j – (9i – 8j) 8 = 0
3 5e = 60
5
= 3i + j e = 12
3
[2] [4]
Cambridge IGCSE
TM
198 Ace Your Additional Mathematics
Answers Add Math.indd 198 14/03/2022 12:29 PM