Calculus Volume 316th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168079
Calculus Volume 3
Solutions for Calculus Volume 3
Problem 183E:
For the following exercises, the vectors u and v are given. Find the cross product uv of the vectors...Problem 184E:
For the following exercises, the vectors u and v are given. Find the cross product uv of the vectors...Problem 185E:
For the following exercises, the vectors u and v are given. Find the cross product uv of the vectors...Problem 186E:
For the following exercises, the vectors u and v are given. Find the cross product uv of the vectors...Problem 187E:
`For the following exercises, the vectors u and v are given. Find the cross product uv of the...Problem 188E:
For the following exercises, the vectors u and v are given. Find the cross product uv of the vectors...Problem 189E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 190E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 191E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 192E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 193E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 194E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 195E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 196E:
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the...Problem 197E:
Calculate the determinant |ijk117203| .Problem 198E:
Calculate the determinant |ijk034161| .Problem 199E:
For the following exercises, the vector u and v are given. Use determinant mutation to find vector w...Problem 200E:
For the following exercises, the vector u and v are given. Use determinant mutation to find vector w...Problem 203E:
[T] Use the cross product uv to find the acute angle between vectors u and v, where u=i+2j and...Problem 204E:
[T] Use the cross product uv to find the obtuse angle between vectors u and v , where u=i+3j+k and...Problem 205E:
Use the sine and cosine of the angle between two nonzero vectors u and v to prove Lagrange’s...Problem 207E:
Nonzero vectors u and v are called collinear if there exists a nonzero scalar such that v=u. Show...Problem 208E:
Nonzero vectors u and v are called collinear if there exists a nonzero scalar a such that v=u. Show...Problem 211E:
Consider paints A(3,1,2),B(2,1,5), and C(1,2,2). Find the area of parallelogram ABCD with adjacent...Problem 212E:
Consider points A(2,3,4),B(0,1,2), and C(1,2,0). Find the area of parallelogram ABCD with adjacent...Problem 213E:
In the following exercises, vectors u,v, and w are given. Find the triple scalar product u(vw) Find...Problem 214E:
In the following exercises, vectors u,v, and w are given. Find the triple scalar product u(vw) Find...Problem 215E:
In the following exercises, vectors u,v, and w are given. Find the triple scalar product u(vw) Find...Problem 216E:
In the following exercises, vectors u,v, and w are given. Find the triple scalar product u(vw) Find...Problem 217E:
Find vectors a,b, and c with a triple scalar product given by the determinant |123025892|. Determine...Problem 218E:
The triple scalar product of vector a,b, and c is given by the determinant |021014137|. Find vector...Problem 219E:
Consider the parallelepiped with edges OA,OB, and OC, where A(2,1,0),B(1,2,0), and C(0,1,). Find the...Problem 220E:
Consider points A(,0,0),B(0,,0), and C(0,0,), with ,, and positive real numbers. Determine the...Problem 221E:
Let u,v, and w be three-dimensional vectors and c be a real number. Prove the following properties...Problem 222E:
Show that vectors u=1,0,8,v=0,1,6, and w=1,9,3 satisfy the following properties of the cross...Problem 223E:
Nonzero vectors u,v, and w are said to be linearly dependent if one of the vectors is a linear...Problem 224E:
Consider vectors u=1,4,7,v=2,1,4,w=0,9,18, and p=0,9,17. Show that u,v, and w are coplanar by using...Problem 225E:
Consider points A(0,0,2),B(1,0,2),C(1,1,2), and D(0,1,2). Are vectors AB,AC, and AD linearly...Problem 226E:
Show that vectors i+j,ij, and i+j+k are linearly independent—that is, there exist two nonzero real...Problem 227E:
Let u=u1,u2,0 and v=v1,v2,0, be two-dimensional vector. The cross product of vectors u and v is net...Problem 228E:
Consider points P(2,1),Q(4,2) and R(1,2). Find the area of triangle P,Q, and R. Determine the...Problem 229E:
Determine a vector of magnitude 10 perpendicular to the plane passing through the x -axis and point...Problem 230E:
Determine a unit vector perpendicular to the plane passing through the z -axis and point A(3,1,2).Problem 231E:
Consider u and v two three-dimensional vectors. If the magnitude of the cross product vector uv is k...Problem 232E:
[T] Assume that the magnitudes of two nonzero vectors u and v are known. The function f()=uvsin...Problem 234E:
- Solve the w1,0,1=3,0,3, where w=w1,w2,w3 is a nonzero vector with a equation magnitude of 3 .Problem 235E:
[T] A mechanic uses a 12in . wrench to turn a bolt. The wrench makes a 30 angle with the horizontal....Problem 236E:
[T] A boy applies the brakes on a bicycle by applying a downward force of 20lb on the pedal when the...Problem 237E:
[T] Find the magnitude of the force that needs to be applied to the end of a 20-cm wrench located on...Problem 238E:
[T] What is the magnitude of the force required to be applied to the end of a 1-ft wrench at an...Problem 239E:
[T] The fence vector F acting on a proton with all electric charge of 1.610-19C (in coulombs) moving...Problem 240E:
[T] The fence vector F acting on a proton with an electric charge of 1.610-19C moving in a magnetic...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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