- 1.1: If a = (1, 7, 9) and b = (1, 9, 7), then a = b.
- 1.2: If a and b are two vectors in R3 and k and l are real numbers, then...
- 1.3: The displacement vector from P1(1, 0, 1) to P2(5, 3, 2) is (4, 3, 3).
- 1.4: Force and acceleration are vector quantities
- 1.5: Velocity and speed are vector quantities
- 1.6: Displacement and distance are scalar quantities
- 1.7: If a particle is at the point (2, 1) in the plane and moves from th...
- 1.8: The vector (2, 3, 2) is the same as 2i + 3j 2k
- 1.9: A set of parametric equations for the line through (1, 2, 0) that i...
- 1.10: A set of parametric equations for the line through (1, 2, 3) and (4...
- 1.11: The line with parametric equations x = 2 3t, y = t + 1, z = 2t 3 ha...
- 1.12: The two sets of parametric equations x = 3t 1, y = 2 t, z = 2t + 5 ...
- 1.13: The parametric equations x = 2 sin t, y = 2 cost, where 0 t , descr...
- 1.14: The dot product of two unit vectors is 1.
- 1.15: For any vector a in Rn and scalar k, we have ka = k a .
- 1.16: If a, u Rn and u = 1, then projua = (a u)u
- 1.17: For any vectors a, b, c in R3, we have a (b c) = (a b) c.
- 1.18: The volume of a parallelepiped determined by the vectors a, b, c R3...
- 1.19: a b b a is a vector.
- 1.20: (a b) c (a c) b is a scalar
- 1.21: The plane containing the points (1, 2, 1), (3, 1, 0), and (1, 0, 2)...
- 1.22: The plane containing the points (1, 2, 1), (3, 1, 0), and (1, 0, 2)...
- 1.23: If A is a 5 7 matrix and B is a 7 7 matrix, then B A is a 7 5 matrix.
- 1.24: If A = 120 3 102 1 592 0 080 6 , then det A = 2 12 1 52 0 0 0 6 + 9...
- 1.25: If A is an n n matrix, then det (2A) = 2 det A
- 1.26: The surface having equation r = 4 sin in cylindrical coordinates is...
- 1.27: The surface having equation = 4 cos in spherical coordinates is a s...
- 1.28: The surface having equation cos sin = 3 in spherical coordinates is...
- 1.29: The surface having equation = 3 in spherical coordinates is the sam...
- 1.30: The surface whose equation in cylindrical coordinates is z = 2r is ...
- 1.31: To raise a square (n n) matrix A to a positive integer power n, one...
- 1.32: A square matrix A is called nilpotent if An = 0 for some positive p...
- 1.33: The n n matrix Hn whose i jth entry is 1/(i + j 1) is called the Hi...
- 1.34: An idealized version of the Spirograph can be obtained by taking a ...
- 1.35: An idealized version of the Spirograph can be obtained by taking a ...
- 1.36: An idealized version of the Spirograph can be obtained by taking a ...
- 1.37: An idealized version of the Spirograph can be obtained by taking a ...
- 1.38: Exercises 3843 are made feasible through the use of appropriate sof...
- 1.39: Exercises 3843 are made feasible through the use of appropriate sof...
- 1.40: Exercises 3843 are made feasible through the use of appropriate sof...
- 1.41: Exercises 3843 are made feasible through the use of appropriate sof...
- 1.42: Exercises 3843 are made feasible through the use of appropriate sof...
- 1.43: Exercises 3843 are made feasible through the use of appropriate sof...
- 1.44: Consider the solid hemisphere of radius 5 pictured in Figure 1.125....
- 1.45: Consider the solid cylinder pictured in Figure 1.126. (a) Describe ...
Solutions for Chapter 1: Vectors
Full solutions for Vector Calculus | 4th Edition
An identity involving a trigonometric function of u - v
Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic
Distance (on a number line)
The distance between real numbers a and b, or |a - b|
A nonnegative number that specifies how off-center the focus of a conic is
Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.
Frequency table (in statistics)
A table showing frequencies.
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).
The amount of time required for half of a radioactive substance to decay.
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.
See Complex plane.
Events A and B such that P(A and B) = P(A)P(B)
Using the science of statistics to make inferences about the parameters in a population from a sample.
The final digit of a number in a stemplot.
Matrix, m x n
A rectangular array of m rows and n columns of real numbers
Angle measure equal to 1/60 of a degree.
See Additive inverse of a real number and Additive inverse of a complex number.
A procedure for fitting a curve y = a . x b to a set of data.
Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i
p = ƒ(x), where x represents production and p represents price
See n factorial.