Thomas Calculus 13th [Solutions]

Section 12.2 Vectors 883
25. length
2 2 2
|2i j 2 k | 2 1 ( 2) 3, the direction is 2 i + 1 j 2 k 2i j 2k = 3
2 i 1 j 2 k
3 3 3 3 3 3
26. length |9i 2j 6 k | 81 4 36 11, the direction is 9 i 2 j 6 k 9i 2j 6k 11
9 i 2 j 6 k
27. length |5 k | 25 5, the direction is k 5k = 5( k)
11 11 11 11 11 11
28. length
3
i
4
k
9 16
1, the direction is 3 i 4 k 3 i 4 k 1
3 i 4 k
5 5 25 25
5 5 5 5 4 5
29. length
1 1 1 1
2
1
6 6 6 6 2
i j k 3 , the direction is
1 i 1 j 1 k
3 3 3
1 i 1 j 1 k = 1 1 1 1
6 6 6 2
i j k
3 3 3
30. length
1 i 1 j 1 k 1
3 3 3 3
2
+ + 3 1, the direction is
1 i 1 j 1 k
3 3 3
10
1 i 1 j 1 k 1
1 i 1 j 1 k
3 3 3 3 3 3
31. (a) 2i (b) 3k (c)
3 j 2 k (d) 6i 2j 3k
10 5
32. (a) 7j
(b)
i k (c)
1 i 1 j k (d)
3 2 4 2
5 5
4 3
a i a j a k
2 3 6
33.
2 2
| | 12 5 169 13;
v v 1 1
v
v
| | 13 13 (12 i 5 k ) the desired vector is 7
13 (12i
5 k)
34.
1 1 1 3
| v| ; v 1 i 1 j 1 k the desired vector is 3 1 i 1 j 1 k
4 4 4 2 | v| 3 3 3
3 3 3
3i 3j 3k
35. (a) 3i 4j 5k 5 2 3 i 4 j 1 k the direction is 3 i 4 j 1 k
5 2 5 2 2
5 2 5 2 2
(b) the midpoint is 1 , 3, 5
2 2
36. (a) 3i 6j 2k 7 3 i 6 j 2 k the direction is 3 i 6 j 2 k
7 7 7
7 7 7
(b) the midpoint is 5
2 , 1, 6
37. (a) i j k 3 1 i 1 j 1 k the direction is 1 i 1 j 1 k
3 3 3
3 3 3
(b) the midpoint is 5 , 7 , 9
2 2 2
38. (a) 2i 2j 2k 2 3 1 i 1 j 1 k the direction is 1 i 1 j 1 k
3 3 3
3 3 3
(b) the midpoint is (1, 1, 1)
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