Thomas Calculus 13th [Solutions]

882 Chapter 12 Vectors and the Geometry of Space
16. cos 135 , sin 135
1
,
1
2 2
17. P1 P2 (2 5) i (9 7) j 2 ( 1) k 3i 2j k
18. P1 P2 ( 3 1) i (0 2) j (5 0) k 4i 2j 5k
19. AB 10 ( 7) i 8 ( 8) j (1 1) k 3i 16j
20. AB ( 1 1) i (4 0) j (5 3) k 2i 4j 2k
21. 5u v 5 1, 1, 1 2, 0, 3 5, 5, 5 2, 0, 3 5 2, 5 0, 5 3 3, 5, 8 3i 5j 8k
22. 2u 3v 2 1, 0, 2 3 1, 1,1 2, 0, 4 3, 3, 3 5, 3, 1 5i 3j k
23. The vector v is horizontal and 1 in. long. The vectors u and w are 11
16
a 45 angle with the horizontal. All vectors must be drawn to scale.
(a)
(b)
in. long. w is vertical and u makes
(c)
(d)
24. The angle between the vectors is 120 and vector u is horizontal. They are all 1 in. long. Draw to scale.
(a)
(b)
(c)
(d)
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