Page 68 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Answers

Chapter 6 Vectors 12. 339 unit 2
Exercise 6.1 13. 29 unit 2
3
1. (a) 4 i – j (b) 5 i + 12 j 14. 6 unit 2
5 5 13 13 2
(c) – 2 i – 1 j 15. –i + j – k
5 5
2. 12i – 5j 16. l = 7 3
6
3
3. (a) 2 i + j – k (b) –4i – 6j + 12k –i + 2j + 8k
7 7 7 17.
69
4. 5i – 2j + k ; 30 units Exercise 6.4
5. –4 i + 1 j + 3 k
26 26 26 1. (a) L : r = 2i – j + 6k + li
1
(b) L : r = –4i + 3k + lj
2
6. 6i + 3j + 7k (c) L : r = 3j – k + lk
3
7. (a) 21 units (b) 5 units (c) 3 units (d) L : r = 2i – 5j + l(–i + 6j)
4
8. (a) 6 untis (b) 7 units (c) 186 units (e) L : r = –2i + j – 3k + l(i + 2j – k)
5
9. (a) No (b) Yes (c) Yes 2. (a) r = 2i + 3k + l(i – j + k)
11. (a) 2i – 2j + 2k, i – 9k (b) r = i + 2j + 2k + l(i – 4j – 2k)
(c) r = 3i + j + 4k + l(–4i + j + k)
(b) 3(i – j + k)
Exercise 6.2 3. x – 1 = y + 3 = z – 2 (=l)
6
–2
5
1. (a) –2i – 8j (b) 16i + 36j 4. r = i – 5j + 2k + l(–3i + 2j + 6k)
(c) 7 (3i + 2j) (d) –35i – 14j 5. r = –i – 2j – 5k + l(7i + 2j – 3k)
4
(e) 6i + 3j 6. (a) r = 2i + j – k + l(3i + j + 6k)
(b) r = 6i – 2j + k + l(i + 5j + k)
2. u – 2v
3. (a) i + j + 5k (b) 1 2 (–i + j + 23k) 7. (a) r = i – 3j + 2k + l(i – j + 5k);
x – 1
z – 2
y + 3
(c) –12i – 7j + 10k 1 = –1 = 5
4. (a) (–1, 3, 0) (b) (–2, 0, –8) (b) r = i + 2j + k + l(i + 2j – 3k);
(c) (–3, 3, –8) (d) (2, –4, 3) x – 1 = y – 2 = z – 1
–3
2
1
5. (a) (5, –6, –1) (b) (0, 2, –3) 8. r = (2i – j + 5k) + l(–3i + 5j – 2k);
(c) (–1, 0, 5) (d) (0, 0, –4) x – 2 y + 1 z – 5
(e) (0, 9, 0) –3 = 5 = –2 (=l)
7. l = 4, l = 1, l = –2 9. p = –1, q = –5
1 2 3
9. 17i – 3j – 10k 10. r = i – 3j + l(2i + j)
398 Exercise 6.5
10. 3i – k 1. r · (i – j – 3k) = –7, x – y – 3z = –7
10 2. r · (i – 2j – k) = –12, x – 2y – z = –12
Exercise 6.3 3. r · (i – 3j – 5k) = 7
1. (a) –23 (b) 5 (c) –9 4. r · (–10i + 10j – 14k) = –32; –10x + 10y – 14z = –32
(d) 6 (e) 18 5. r · (6i + 2j – 3k) = 17
2. (a) 7°8´ (b) 90° (c) 75°38´ 6. r · (i + 2j + 2k) = –6, x + 2y + 2z = –6
(d) 73°24´ (e) 90° 7. r · (2i – 3j + k) = 9, 2x – 3y + z = 9
3. 80°24´ 8. r · (i – 3j + 2k) = 0, x – 3y + 2z = 0
4. (a) –32 (b) 130°46´ Exercise 6.6
5. 60° 1. (a) 71°34´ (b) 0°
6. (a) orthogonal (b) orthogonal 2. 71°14´
(c) orthogonal 3. 70°32´
7. –2 4. 80°24´
→ 5. 61°1´
9. (a) OM = 6i + 6j + 12k ; 6. 79°6´
→
NM = –6i + 2j + 12k 7. 22°12´
(b) 53.0° 8. 71°34´
10. –5i + 7j – 3k 9. 90°
11. (a) –4i + 72j + 28k (b) 4i – 72j – 28k 10. 49°59´ ≈ 50°

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Answers STPM Math T S1.indd 287 3/28/18 4:25 PM