INDEX Q 455
Vectors; dot product of (Cont.):
40.55 to 40.58, 40.60 to 40.67,
43.1 to 43.7, 43.10 to 43.12,
43.16,43.17,43.66,45.9,
45.13 to 45.15, 45.35, 45.37,
45.39,45.41,45.43,45.45to
45.49
length of, 33.3, 33.13, 40.26
lines and, 33.7, 33.8
magnitude of, 33.3, 33.13
multiplication by scalars, 33.2,
40.30
normal, 42.105 to 42.115, 42.122
to 42.126, 45.19
parallel, 33.4, 33.5, 33.36, 33.39,
40.68
parallelogram law for, 33.17
perpendicular, 33.4 to 33.8,
33.12, 33.18,33.19, 33.21,
33.31, 33.32, 33.37, 33.39,
40.36,40.39,40.41,40.42,
40.51, 40.68
planes and, 40.106 to 40.108
position, 34.44 to 34.56, 34.59,
34.60, 34.65 to 34.72, 34.74
to 34.81, 34.82 to 34.96,
34.100,34.101,34.103,
34.105 to 34.108, 45.1,45.2,
45.4 to 45.6, 45.12, 45.15 to
45.23
principal unit normal, 34.81 to
34.86, 34.88, 34.90, 34.91,
34.105 to 34.107, 45.16
rectangular form of, 33.14 to
33.16
scalar projection of, 33.4, 40.33
Vectors (Cont.):
surface normal, 42.31
tangent, 34.44 to 34.56, 34.59,
34.60, 34.65 to 34.72, 34.74 to
34.80,34.89,34.92,42.118,
42.119, 45.1, 45.3 to 45.6
triangle inequality for, 33.29
unit, 33.24, 34.67, 40.28, 40.31,
40.33, 40.40, 40.54, 43.66
unit tangent, 34.47 to 34.50, 34.81
to 34.93, 34.105 to 34.107
vector projection of, 33.4, 33.20,
33.39, 40.33
velocity, 34.44 to 34.56, 34.59,
34.60, 34.65 to 34.72, 34.74
to 34.80, 34.89, 34.92,45.1,
45.2, 45.4 to 45.6, 45.12,
45.15 to 45.23
zero, 33.11
Velocity, escape, 19.95, 19.96
Velocity vector, 34.44 to 34.56,
34.59, 34.60, 34.65 to 34.72,
34.74 to 34.80, 34.89, 34.92,
45.1,45.2, 45.4 to 45.6,
45.12, 45.15 to 45.23
Vertex of parabolas, 15.30, 21.13,
21.15,21.22, 21.23
Vertices:
parallelogram, 3.28, 40.109
right triangle, 3.25, 3.26, 40.13
triangle, 40.17
Volume:
cone, 14.6, 14.18, 14.29, 14.38,
16.9, 16.42, 22.2, 31.34,
42.86,43.67,44.41,44.51
cone frustrum, 22.49
Volume (Cont.):
cylinder, 14.2, 14.48, 16.7, 16.8,
16.16, 16.18, 16.43,43.67,
44.70
ellipsoid, 41.22
by integration, 22.1 to 22.58,
23.38, 23.59, 24.46, 24.48,
24.49, 27.63, 28.26, 28.27,
28.29 to 28.32, 29.44, 31.33
to 31.35, 32.39, 32.40,44.16
to 44.19, 44.21 to 44.23,
44.29 to 44.32, 44.34, 44.40,
44.41,44.50,44.51, 44.59 to
44.63, 44.66 to 44.70
Pappus's theorem for, 31.33 to
31.35
parallelepiped, 40.45, 40.49,
40.56, 40.63
pyramid, 22.22
of revolution, 31.33 to 31.35
sphere, 14.7, 14.13, 14.35, 14.37,
14.43, 14.48,22.1,44.34,
44.50
spherical segment, 14.41
tetrahedron, 22.23, 42.113
torus, 31.33
Wave equation, 42.55 to 42.58
Wavelength of trigonometric
functions, 10.12
Work, by integration, 31.16 to
31.23, 45.43
Wronskian, 46.65 to 46.69
Zeno's paradox, 37.32
Zero vector, 33.11
Vectors; dot product of (Cont.):
40.55 to 40.58, 40.60 to 40.67,
43.1 to 43.7, 43.10 to 43.12,
43.16,43.17,43.66,45.9,
45.13 to 45.15, 45.35, 45.37,
45.39,45.41,45.43,45.45to
45.49
length of, 33.3, 33.13, 40.26
lines and, 33.7, 33.8
magnitude of, 33.3, 33.13
multiplication by scalars, 33.2,
40.30
normal, 42.105 to 42.115, 42.122
to 42.126, 45.19
parallel, 33.4, 33.5, 33.36, 33.39,
40.68
parallelogram law for, 33.17
perpendicular, 33.4 to 33.8,
33.12, 33.18,33.19, 33.21,
33.31, 33.32, 33.37, 33.39,
40.36,40.39,40.41,40.42,
40.51, 40.68
planes and, 40.106 to 40.108
position, 34.44 to 34.56, 34.59,
34.60, 34.65 to 34.72, 34.74
to 34.81, 34.82 to 34.96,
34.100,34.101,34.103,
34.105 to 34.108, 45.1,45.2,
45.4 to 45.6, 45.12, 45.15 to
45.23
principal unit normal, 34.81 to
34.86, 34.88, 34.90, 34.91,
34.105 to 34.107, 45.16
rectangular form of, 33.14 to
33.16
scalar projection of, 33.4, 40.33
Vectors (Cont.):
surface normal, 42.31
tangent, 34.44 to 34.56, 34.59,
34.60, 34.65 to 34.72, 34.74 to
34.80,34.89,34.92,42.118,
42.119, 45.1, 45.3 to 45.6
triangle inequality for, 33.29
unit, 33.24, 34.67, 40.28, 40.31,
40.33, 40.40, 40.54, 43.66
unit tangent, 34.47 to 34.50, 34.81
to 34.93, 34.105 to 34.107
vector projection of, 33.4, 33.20,
33.39, 40.33
velocity, 34.44 to 34.56, 34.59,
34.60, 34.65 to 34.72, 34.74
to 34.80, 34.89, 34.92,45.1,
45.2, 45.4 to 45.6, 45.12,
45.15 to 45.23
zero, 33.11
Velocity, escape, 19.95, 19.96
Velocity vector, 34.44 to 34.56,
34.59, 34.60, 34.65 to 34.72,
34.74 to 34.80, 34.89, 34.92,
45.1,45.2, 45.4 to 45.6,
45.12, 45.15 to 45.23
Vertex of parabolas, 15.30, 21.13,
21.15,21.22, 21.23
Vertices:
parallelogram, 3.28, 40.109
right triangle, 3.25, 3.26, 40.13
triangle, 40.17
Volume:
cone, 14.6, 14.18, 14.29, 14.38,
16.9, 16.42, 22.2, 31.34,
42.86,43.67,44.41,44.51
cone frustrum, 22.49
Volume (Cont.):
cylinder, 14.2, 14.48, 16.7, 16.8,
16.16, 16.18, 16.43,43.67,
44.70
ellipsoid, 41.22
by integration, 22.1 to 22.58,
23.38, 23.59, 24.46, 24.48,
24.49, 27.63, 28.26, 28.27,
28.29 to 28.32, 29.44, 31.33
to 31.35, 32.39, 32.40,44.16
to 44.19, 44.21 to 44.23,
44.29 to 44.32, 44.34, 44.40,
44.41,44.50,44.51, 44.59 to
44.63, 44.66 to 44.70
Pappus's theorem for, 31.33 to
31.35
parallelepiped, 40.45, 40.49,
40.56, 40.63
pyramid, 22.22
of revolution, 31.33 to 31.35
sphere, 14.7, 14.13, 14.35, 14.37,
14.43, 14.48,22.1,44.34,
44.50
spherical segment, 14.41
tetrahedron, 22.23, 42.113
torus, 31.33
Wave equation, 42.55 to 42.58
Wavelength of trigonometric
functions, 10.12
Work, by integration, 31.16 to
31.23, 45.43
Wronskian, 46.65 to 46.69
Zeno's paradox, 37.32
Zero vector, 33.11