Solutions for Multivariable Calculus
Problem 1E:
CONCEPT CHECK Scalar and Vector Describe the difference between a scalar and a vector. Give example...Problem 2E:
CONCEPT CHECK Vector Two points and a vector are given. Determine which point is the initial point...Problem 3E:
Sketching a Vector In Exercises 3 and 4, (a) find the component form of the vector v and (b) sketch...Problem 5E:
Equivalent Vectors In Bunches 5-8, find the vector: u and v whose initial and terminal points are...Problem 6E:
Equivalent Vectors In Bunches 5-8, find the vector: u and v whose initial and terminal points are...Problem 7E:
Equivalent Vectors In Bunches 5-8, find the vector: u and v whose initial and terminal points are...Problem 8E:
Equivalent Vectors In Bunches 5-8, find the vector: u and v whose initial and terminal points are...Problem 9E:
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v...Problem 10E:
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v...Problem 11E:
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v...Problem 12E:
Writing a Vector in Different Forms to Exercises 9-16, the initial and terminal points of a vector v...Problem 14E:
Writing a Vector in Different Forms to Exercises 9-16, the initial and terminal points of a vector v...Problem 15E:
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v...Problem 16E:
Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v...Problem 17E:
Finding a Terminal Point In Exercise 17 and 18, the vector v and its initial point are given. Find...Problem 18E:
Finding a Terminal Point In Exercise 17 and 18, the vector v and its initial point are given. Find...Problem 25E:
Sketching Scalar MultipliesIn Exercises 25 and 26, sketch each scalar multiple of v. v=3,5 (a) 2v...Problem 26E:
Sketching Scalar MultipliesIn Exercises 25 and 26, sketch each scalar multiple of v. v=2,3 (a) 4v...Problem 27E:
Using Vector Operations In Exercise 27 and 28, And (a) 23u , (b) 3v, (c) vu (d) 2u+5v. u=4,9,v=2,5Problem 28E:
Using Vector Operations In Exercise 27 and 28, And (a) 23u , (b) 3v, (c) vu (d) 2u+5v. u=3,8,v=8,7Problem 29E:
Sketching a Vector In Exercises 29-34, use the figure to sketch a graph of the vector. To print an...Problem 31E:
Sketching a Vector In Exercises 29-34, use the figure to sketch a graph of the vector. To print an...Problem 32E:
Sketching a Vector In Exercises 29-34, use the figure to sketch a graph of the vector. To print an...Problem 33E:
Sketching a Vector In Exercises 29-34, use the figure to sketch a graph of the vector. To print an...Problem 35E:
Finding a Unit Vector In Exercises 35-38, find the unit vector in the direction of v and verify that...Problem 36E:
Finding a Unit Vector In Exercises 35-38, find the unit vector in the direction of v and verify that...Problem 37E:
Finding a Unit Vector In Exercises 35-38, find the unit vector in the direction of v and verify that...Problem 38E:
Finding a Unit Vector In Exercises 35-38, find the unit vector in the direction of v and verify that...Problem 39E:
Finding MagnitudesIn Exercises 3942, find the following. (a) u (b) v (c) u+v (d) uu (e) vv (f)...Problem 41E:
Finding MagnitudesIn Exercises 3942, find the following. (a) u (b) v (c) u+v (d) uu (e) vv (f)...Problem 43E:
Using the Triangle Inequality In Exercises 43 und 44, sketch a graph of u, v, and u+v. Then...Problem 46E:
Finding a Vector In Exercises 45-48, find the vector v with the given magnitude and the same...Problem 53E:
Finding a Vector In Exercises 53-56, find the component form of u+v given the lengths of u and v and...Problem 54E:
Finding a Vector In Exercises 53-56, find the component form of u+v given the lengths of u and v and...Problem 55E:
Finding a Vector In Exercises 53-56, find the component form of u+v given the lengths of u and v and...Problem 56E:
Finding a Vector In Exercises 53-56, find the component form of u+v given the lengths of u and v and...Problem 60E:
HOW DO YOU SEE IT? Use the figure to determine whether each statement is true or false. Justify your...Problem 61E:
Finding Values In Exercises 61-66, And a and b such that v=au+bw, where u=1,2 and w=1,1. v=4,5Problem 67E:
Finding Unit VectorsIn Exercises 6772, find a unit vector (a) parallel to and (b) perpendicular to...Problem 71E:
Finding Unit Vectors In Exercises 67-72, find a unit vector (a) parallel to and (b) perpendicular to...Problem 76E:
Numerical and Graphical Analysis Forces with magnitudes of 180 newtons and 275 newtons act on a hook...Problem 79E:
Cable Tension In Exercises 79 and 80, determine the tension in the cable supporting the given load.Problem 80E:
Cable TensionIn Exercises 79 and 80, determine the tension in the cable supporting the given load.Problem 81E:
Projectile Motion A gun with a muzzle velocity of 1200 feet per second is fired at an angle of 6...Problem 83E:
Navigation A plane is flying with a bearing of 302. Its speed with respect to the air is 900...Problem 84E:
NavigationA plane flies at a constant groundspeed of 400 miles per hour due east and encounters a...Problem 90E:
True or False? In Exercises 85-94, determine whether the statement is true or false. If it is false,...Browse All Chapters of This Textbook
Chapter 11 - Vectors And The Geometry Of SpaceChapter 11.1 - Vectors In The PlaneChapter 11.2 - Space Coordinates And Vectors In SpaceChapter 11.3 - The Dot Product Of Two VectorsChapter 11.4 - The Cross Product Of Two Vectors In SpaceChapter 11.5 - Lines And Planes In SpaceChapter 11.6 - Surfaces In SpaceChapter 11.7 - Cylindrical And Spherical CoordinatesChapter 12 - Vector-valued FunctionsChapter 12.1 - Vector-valued Functions
Chapter 12.2 - Differentiation And Integration Of Vector-valued FunctionsChapter 12.3 - Velocity And AccelerationChapter 12.4 - Tangent Vectors And Normal VectorsChapter 12.5 - Arc Length And CurvatureChapter 13 - Functions Of Several VariablesChapter 13.1 - Introduction To Functions Of Several VariablesChapter 13.2 - Limits And ContinuityChapter 13.3 - Partial DerivativesChapter 13.4 - DifferentialsChapter 13.5 - Chain Rules For Functions Of Several VariablesChapter 13.6 - Directional Derivatives And GradientsChapter 13.7 - Tangent Planes And Normal LinesChapter 13.8 - Extrema Of Functions Of Two VariablesChapter 13.9 - Applications Of ExtremaChapter 13.10 - Lagrange MultipliersChapter 14 - Multiple IntegrationChapter 14.1 - Iterated Integrals And Area In The PlaneChapter 14.2 - Double Integrals And VolumeChapter 14.3 - Change Of Variables: Polar CoordinatesChapter 14.4 - Center Of Mass And Moments Of InertiaChapter 14.5 - Surface AreaChapter 14.6 - Triple Integrals And ApplicationsChapter 14.7 - Triple Integrals In Other CoordinatesChapter 14.8 - Change Of Variables: JacobiansChapter 15 - Vector AnalysisChapter 15.1 - Vector FieldsChapter 15.2 - Line IntegralsChapter 15.3 - Conservative Vector Fields And Independence Of PathChapter 15.4 - Green’s TheoremChapter 15.5 - Parametric SurfacesChapter 15.6 - Surface IntegralsChapter 15.7 - Divergence TheoremChapter 15.8 - Stokes’s TheoremChapter 16 - Additional Topics In Differential EquationsChapter 16.1 - Exact First-order EquationsChapter 16.2 - Second-order Homogeneous Linear EquationsChapter 16.3 - Second-order Nonhomogeneous Linear EquationsChapter 16.4 - Series Solutions Of Differential Equations
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Multivariable Calculus (looseleaf)
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