Thomas Calculus 13th [Solutions]

902 Chapter 12 Vectors and the Geometry of Space
i j k
33. S(0, 0,12), P (0, 0, 0) and v 4i 2j 2k PS v 0 0 12 24i 48j 24 i 2j
4 2 2
d
PS v
24 1 4 24 5
| v| 16 4 4 24
5 24 2 30
is the distance from S to the line
i j k
34. S(0, 0, 0), P (5, 5, 3) and v 3i 4j 5k PS v 5 5 3 13i 16j 5k
3 4 5
d
PS v
169 256 25 450
| v| 9 16 25 50
9 3
is the distance from S to the line
PS v
35. S(2, 1, 3), P (2, 1, 3) and v 2i 6j PS v 0 d
0 0 is the distance from S to the line
| v| 40
(i.e., the point S lies on the line)
i j k
36. S(2, 1, 1), P (0, 1, 0) and v 2i 2j 2k PS v 2 0 1 2i 6j 4k
2 2 2
d
PS v
4 36 16 56 14
| v| 4 4 4 12 3
is the distance from S to the line
i j k
37. S(3, 1, 4), P (4, 3, 5) and v i 2j 3k PS v 1 4 9 30i 6j 6k
1 2 3
d
PS v
900 36 36 972 486 81 6 9 42
| v| 1 4 9 14 7 7 7
is the distance from S to the line
i j k
38. S( 1, 4, 3), P (10, 3, 0) and v 4i 4k PS v 11 7 3 28i 56j 28k 28 i 2j k
4 0 4
d
PS v
28 1 4 1
| v| 4 1 1
7 3
is the distance from S to the line
39. S(2, 3, 4), x 2y 2z 13 and P (13, 0, 0) is on the plane PS 11i 3j 4k and n i 2j 2k
d PS n 11 6 8 9
| n| 1 4 4 9
3
40. S(0, 0, 0), 3x 2y 6z 6 and P (2, 0, 0) is on the plane PS 2i and n 3i 2j 6k
d PS n 6 6 6
| n|
9 4 36 49 7
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