Page 314 - Matematik Tambahan Tingkatan 4 KSSM

(c) |p| = 5 unit |q| = 8.602 unit | r| = 5.099 unit
Latih Diri 8.5 ~ ~ ~
Latih Diri 8.8
1. (a) (b)
2 + v
u
∼ ∼ 1. (a) 3.606 unit (b) 8.062 unit
1 _ + 2 u
v
2 ∼ ∼ 4
(c) 7 unit (d) 13 unit
(c) (d) (e) 6 unit
u − 2 v ∼ 3i + 2j –i – 9j
∼
3 _
2 u − v ∼ 2. (a) ~ ~ (b) ~ ~
∼
2 13 82
2. 131.19°, 106.30 km j −1 –8i – 15j
2 (c) i (d) ~ ~
3. (a) y (b) –x + y ~ 17
3~ ~ ~ 3. (a) Vektor unit (b) Vektor unit
1 2
(c) y – x (d) – y – x (c) Vektor unit (d) Bukan vektor unit
3~ ~ 3~ ~ 4. (a) ±1 (b) ±1
4. (a) 578.27 km j –1 (b) 345.07° 1
(c) 0 (d) ±
Latih Diri 8.6 2
30 (e) ±0.866 (f) ±0.988
1. k = 5. p = ±3
7
→ →
2k − k
2. (a) BD = –24x + 20y, AE = 6x + 15y 6. h = ± 2
~ ~ ~ ~
Latihan Intensif 8.2 Latih Diri 8.9
16
–9
1. (a) y + x (b) –y + x 1. (a) ( 30) (b) ( –47)
~ ~ ~ ~
1
(c) x + y
12
7
~ 2~ (c) ( –13) (d) ( 16)
2. (a) 3x + y (b) y – 2x
~ ~ ~ ~
(c) –y + 2x 2. (a) 10i + 18j ~ (b) 2i + 6j ~
~
~
~ ~
3. –a + b 4. h = –10, k = 23 (c) –7i – 26j (d) 5.5i + 20j
~
~
~
~
~
~
5. 6.47 m s –1
Latih Diri 8.10
3
6. (a) (i) –b + a (ii) (–b + a)
~ ~ 5 ~ ~ 2
2 3 3 1. ( −9.5)
(iii) b + a (iv) –b + a
5 ~ 5 ~ ~ 4 ~ 30 10
2 3 3 2. Bot A = ( 15) , Bot B = ( 10)
(b) (i) λb + λa (ii) (1 – µ)b + µa
5 ~ 5 ~ ~ 4 ~ Kedua-dua bot tidak akan bertembung.
5 2
(c) λ = , µ =
6 3 Latihan Intensif 8.3
Latih Diri 8.7 3
→ → → 1. (a) ( 8) (b) 8.544 N
1. (a) OA = 2i + 2j, OF = –8i, BC = –10i + j,
→ ~ ~ → ~ → ~ ~ 2. k = 10 atau 1
FA = 10i + 2j, DE = 14i, DO = –j 23
~
~
~
→ 2 → –8 → –10 ~ → 10 3. m = , |u| : |v| = 9 : 16
(b) OA = ( 2) , OF = ( 0) , BC = ( 1 ) , FA = ( 2) , 3 ~ ~ 4i + 3j
→
→ 14 → 0 4. (a) BC = 8i + 6j (b) ~ ~
DE = ( 0) , DO = ( –1) → ~ ~ 5
→ 5 (c) AR = 6i + 2j
~
2. (a) OB = ( 8) (b) 8.602 unit −1 ~
→ → 5. 2.96 km j , 101.69°
3. (a) (i) AB = 4i + j (ii) BA = –4i – j 6

→ ~ ~ → ~ ~ 6. (a) (b)
(iii) BC = –i – 5j (iv) DC = 2i (c) 4 5
→ ~ ~ → ~
(v) AC = 3i – 4j (vi) AB = 4i + j 7. ± 1 atau ± 2
→ → ~ ~ ~ ~
(b) AB dan DE, kerana mempunyai kecerunan 2 2
yang sama. 8. –2 5 i + 5 j
→ → ~ ~
(c) BA dan DE, kerana mempunyai arah bertentangan. 4 – n
4. (a) p = 3i – 4j (b) P(3, – 4), Q(–5, –7), 9. m =
~ ~ ~ 4
q = –5i – 7j R(1, 5) 10. (a) (50 – 4t)i + (20 + 4t)j
~ ~ ~ ~ ~
r = i + 5j (b) Selepas 5 jam
~ ~ ~
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