Thomas Calculus 13th [Solutions]

Section 12.3 The Dot Product 891
40. v 3i 2j is parallel to the line 2x 3 y c;
P (1, 3) on the line ( 2)(1) (3)(3) c
2x 3y 11 or 2x
3y
11
41. P (0, 0), Q (1, 1) and F 5j PQ i j and W F PQ (5 j) ( i j) 5 N m 5 J
42. W | F | (distance) cos (602,148 N)(605 km)(cos 0) 364,299,540 N km (364,299,540)(1000) N m
11
3.6429954 10 J
43. W | F| PQ cos (200)(20)(cos30 ) 2000 3 3464.10 N m 3464.10 J
44. W | F| PQ cos (1000)(5280)(cos60 ) 2,640,000 ft lb
In Exercises 45-50 we use the fact that n ai bj is normal to the line ax by c.
1 1 2 1
45. n1 3i j and 6 1 1 1
2 2 cos n n
n i j
| n1|| n2| cos cos
10 5 2 4
1 1 2 1
46. n1 3i j and 3 1 1 1 2
2 3 cos n n
n i j
| n1 || n2
| cos cos
4 4
2 3
1 1 2 1 3 3 1 3
47. n1 3i j and 2 3 cos n n
n i j
| n1 || n2
| cos cos
4 4
2 6
1 n1 n2
1 1 3 3 3
48. n1 i 3j and n2 1 3 i 1 3 j cos cos
| n1 || n2
|
1 3 1 2 3 3 1 2 3 3
1 4 1
cos cos 1
2 8 2 4
1 2
49. n1 3i 4j and n 1 1 3 4 1 7
2 i j cos n n
| n1 || n2
| cos cos 0.14 rad
25 2 5 2
1 2
50. n1 12i 5j and n 1 1 24 10 1 14
2 2i 2j cos n n
| n1 || n2
| cos cos 1.18 rad
169 8 26 2
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