Calculus Volume 316th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168079
Calculus Volume 3
Solutions for Calculus Volume 3
Problem 61E:
Consider a rectangular box with one of the vertices at the origin, as shown in the following figure....Problem 63E:
For the following exercises, describe and graph the set of points that satisfles the given equation....Problem 64E:
For the following exercises, describe and graph the set of points that satisfles the given equation....Problem 65E:
For the following exercises, describe and graph the set of points that satisfles the given equation....Problem 66E:
For the following exercises, describe and graph the set of points that satisfles the given equation....Problem 67E:
Write the equation of the plane passing through point (1,1,1) that is parallel to the xy -plane.Problem 68E:
Write the equation of the plane passing through point (1,3,2) that is parallel to the xz -plane.Problem 71E:
For the following exercises, find the equation of the sphere in standard form that satisfies the...Problem 72E:
For the following exercises, find the equation of the sphere in standard form that satisfies the...Problem 73E:
For the following exercises, find the equation of the sphere in standard form that satisfies the...Problem 74E:
For the following exercises, find the equation of the sphere in standard form that satisfies the...Problem 75E:
For the following exercises, find the center and radius of the sphere with an equation in general...Problem 76E:
For the following exercises, find the center and radius of the sphere with an equation in general...Problem 77E:
For the following exercises, express vector PQ with the initial paint at P and the terminal point at...Problem 78E:
For the following exercises, express vector PQ with the initial paint at P and the terminal point at...Problem 79E:
For the following exercises, express vector PQ with the initial paint at P and the terminal point at...Problem 80E:
For the following exercises, express vector PQ with the initial paint at P and the terminal point at...Problem 81E:
For the following exercises, express vector PQ with the initial paint at P and the terminal point at...Problem 82E:
For the following exercises, express vector PQ with the initial paint at P and the terminal point at...Problem 83E:
For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,...Problem 84E:
For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,...Problem 85E:
For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,...Problem 86E:
For the following exercises, use the given vectors a and b to find and express the vectors a+b,4a ,...Problem 87E:
For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u ....Problem 88E:
For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u ....Problem 89E:
For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u ....Problem 90E:
For the following exercises, vectors u and v are given. Find the magnitudes of vectors u-v and -2u ....Problem 91E:
For the following exercises, find the unit vector in the direction of the given vector a and express...Problem 92E:
For the following exercises, find the unit vector in the direction of the given vector a and express...Problem 93E:
For the following exercises, find the unit vector in the direction of the given vector a and express...Problem 94E:
For the following exercises, find the unit vector in the direction of the given vector a and express...Problem 95E:
For the following exercises, find the unit vector in the direction of the given vector a and express...Problem 96E:
For the following exercises, find the unit vector in the direction of the given vector a and express...Problem 97E:
Determine whether AB and PQ are equivalent vectors, where A(1,1,1),B(3,3,3),P(1,4,5), and Q(3,6,7) .Problem 98E:
Determine whether the vectors AB and PQ are equivalent, where A(1,4,1),B(2,2,0),P(2,5,7), and...Problem 99E:
For the following exercises, find vector u with a magnitude that is given and satisfies the given...Problem 100E:
For the following exercises, find vector u with a magnitude that is given and satisfies the given...Problem 101E:
For the following exercises, find vector u with a magnitude that is given and satisfies the given...Problem 102E:
For the following exercises, find vector u with a magnitude that is given and satisfies the given...Problem 103E:
Determine a vector of magnitude 5 in the direction of vector AB , where A(2,1,5) and B(3,4,-7) .Problem 104E:
Find a vector of magnitude 2 that points in the opposite direction than vector AB , where A(1,1,1)...Problem 105E:
Consider the points A(2,,0),B(0,1,), and C(1,1,), where and are negative real numbers. Find and ...Problem 106E:
Consider points A(,0,0),B(0,,0), and C(,,), where and are positive real numbers. Find and such...Problem 107E:
Let P(x,y,z) be a point situated at an equal distance from points A(1,1,0) and B(1,2,1) . Show that...Problem 108E:
Let P(x,y,z) be a point situated at an equal distance from the origin and point A(4,1,2) . Show that...Problem 109E:
The points A,B, and C are collinear (in this order) if the relation AB+BC=AC is satisfied. Show that...Problem 111E:
[T] A force F of 50N acts on a particle in the direction of the vector OP , where P(3,4,0) . a....Problem 112E:
[T] A force F of 40N acts on a box in the direction of the vector OP , where P(1,0,2) . a. Express...Problem 113E:
If F is a force that moves an object from point P1(x1,y1,z1) to another point P2(x2,y2,z2) , then...Problem 114E:
A box is pulled 4 yd horizontally in the x -direction by a constant force F . Find the displacement...Problem 115E:
The sum of the forces acting on an object is called the resultant or net force. All abject is said...Problem 116E:
[T] Let Fk=1,k,k2,k=1,...,n be n forces acting on a particle, with n2 . a. Find the net force...Problem 117E:
The force of gravity F acting on an object is given by F=mg, where m is the mass of the object...Problem 118E:
A 5-kg pendant chandelier is designed such that the alabaster bowl is held by four chains of equal...Problem 119E:
[T] A 30-kg block of cement is suspended by three cables of equal length that are anchored at points...Problem 120E:
Two soccer players are practicing for an upcoming game. One of them runs 10m from point A to point B...Browse All Chapters of This Textbook
Chapter 1 - Parametric Equations And Polar CoordinatesChapter 1.1 - Parametric EquationsChapter 1.2 - Calculus Of Parametric CurvesChapter 1.3 - Polar CoordinatesChapter 1.4 - Area And Arc Length In Polar CoordinatesChapter 1.5 - Conic SectionsChapter 2 - Vectors In SpaceChapter 2.1 - Vectors In The PlaneChapter 2.2 - Vectors In Three DimensionsChapter 2.3 - The Dot Product
Chapter 2.4 - The Cross ProductChapter 2.5 - Equations Of Lines And Planes In SpaceChapter 2.6 - Quadric SurfacesChapter 2.7 - Cylindrical And Spherical CoordinatesChapter 3 - Vector-valued FunctionsChapter 3.1 - Vector-valued Functions And Space CurvesChapter 3.2 - Calculus Of Vector-valued FunctionsChapter 3.3 - Arc Length And CurvatureChapter 3.4 - Motion In SpaceChapter 4 - Differentiation Of Functions Of Several VariablesChapter 4.1 - Functions Of Several VariablesChapter 4.2 - Limits And ContinuityChapter 4.3 - Partial DerivativesChapter 4.4 - Tangent Planes And Linear ApproximationsChapter 4.5 - The Chain RuleChapter 4.6 - Directional Derivatives And The GradientChapter 4.7 - Maxima/minima ProblemsChapter 4.8 - Lagrange MultipliersChapter 5 - Multiple IntegrationChapter 5.1 - Double Integrals Over Rectangular RegionsChapter 5.2 - Double Integrals Over General RegionsChapter 5.3 - Double Integrals In Polar CoordinatesChapter 5.4 - Triple IntegralsChapter 5.5 - Triple Integrals In Cylindrical And Spherical CoordinatesChapter 5.6 - Calculating Centers Of Mass And Moments Of InertiaChapter 5.7 - Change Of Variables In Multiple IntegralsChapter 6 - Vector CalculusChapter 6.1 - Vector FieldsChapter 6.2 - Line IntegralsChapter 6.3 - Conservative Vector FieldsChapter 6.4 - Green's TheoremChapter 6.5 - Divergence And CurlChapter 6.6 - Surface IntegralsChapter 6.7 - Stokes' TheoremChapter 6.8 - The Divergence TheoremChapter 7 - Second-order Differential EquationsChapter 7.1 - Second-order Linear EquationsChapter 7.2 - Nonhomogeneous Linear EquationsChapter 7.3 - ApplicationsChapter 7.4 - Series Solutions Of Differential Equations
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