Calculus Volume 316th EditionGilbert Strang, Edwin Jed Herman Publisher: OpenStaxISBN: 9781938168079
Calculus Volume 3
Solutions for Calculus Volume 3
Problem 123E:
For the following exercises, the vectors u and v are given. Calculate the dot product uv . 123....Problem 124E:
For the following exercises, the vectors u and v are given. Calculate the dot product uv . 124....Problem 125E:
For the following exercises, the vectors u and v are given. Calculate the dot product uv . 125....Problem 126E:
For the following exercises, the vectors u and v are given. Calculate the dot product uv . 126....Problem 127E:
For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b...Problem 128E:
For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b...Problem 129E:
For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b...Problem 130E:
For the following exercises, the vectors a,b, and c are given. Determine the vectors (ab)c and (ac)b...Problem 131E:
For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the...Problem 132E:
For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the...Problem 133E:
For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the...Problem 134E:
For the following exercises, the two-dimensional vectors a and b are given. Find the measure of the...Problem 135E:
For the following exercises, find the measure 0f the angle between the three-dimensional vectors a...Problem 136E:
For the following exercises, find the measure 0f the angle between the three-dimensional vectors a...Problem 137E:
For the following exercises, find the measure 0f the angle between the three-dimensional vectors a...Problem 138E:
For the following exercises, find the measure 0f the angle between the three-dimensional vectors a...Problem 139E:
For the following exercises, find the measure 0f the angle between the three-dimensional vectors a...Problem 140E:
For the following exercises, find the measure 0f the angle between the three-dimensional vectors a...Problem 141E:
For the following exercises determine whether the given vectors are orthogonal. 141. a=x,y,z,b=y,x,...Problem 142E:
For the following exercises determine whether the given vectors are orthogonal. 142. a=x,x,b=y,y,...Problem 143E:
For the following exercises determine whether the given vectors are orthogonal. 143....Problem 144E:
For the following exercises determine whether the given vectors are orthogonal. 144. a=ij,b=7i+2jkProblem 145E:
For the following exercises determine whether the given vectors are orthogonal. 145. Find all...Problem 146E:
For the following exercises determine whether the given vectors are orthogonal. 146. Find all...Problem 147E:
For the following exercises determine whether the given vectors are orthogonal. 147. Determine all...Problem 148E:
For the following exercises determine whether the given vectors are orthogonal. 148. Determine all...Problem 149E:
For the following exercises determine whether the given vectors are orthogonal. 149. Determine the...Problem 150E:
For the following exercises determine whether the given vectors are orthogonal. 150. Determine the...Problem 151E:
[T] Consider the points P(4,5) and Q(5,7) . Determine vectors OP and OQ . Express the answer by...Problem 152E:
[T] Consider points A(1,1),B(2,7) , and C(6,3). Determine vector BA and BC . Express the answer in...Problem 153E:
Determine the measure of angle A in triangle ABC , where A(1,1,8),B(4,3,4), and C(3,1,5). Express...Problem 154E:
Consider points P(3,7,2) and Q(1,1,3). Determine the angle between vectors OP and OQ . Express the...Problem 155E:
For the following exercises, determine which (if any) pairs of the following vectors are orthogonal....Problem 156E:
For the following exercises, determine which (if any) pairs of the following vectors are orthogonal....Problem 157E:
For the following exercises, determine which (if any) pairs of the following vectors are orthogonal....Problem 158E:
For the following exercises, determine which (if any) pairs of the following vectors are orthogonal....Problem 159E:
For the following exercises, determine which (if any) pairs of the following vectors are orthogonal....Problem 160E:
For the following exercises, determine which (if any) pairs of the following vectors are orthogonal....Problem 161E:
For the following problems, the vector u is given. Find the direction cosines for the vector u ....Problem 162E:
For the following problems, the vector u is given. Find the direction cosines for the vector u ....Problem 163E:
For the following problems, the vector u is given. Find the direction cosines for the vector u ....Problem 164E:
For the following problems, the vector u is given. Find the direction cosines for the vector u ....Problem 165E:
For the following problems, the vector u is given. Find the direction cosines for the vector u ....Problem 166E:
For the following problems, the vector u is given. Find the direction cosines for the vector u ....Problem 167E:
For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of...Problem 168E:
For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of...Problem 169E:
For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of...Problem 170E:
For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of...Problem 171E:
For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of...Problem 172E:
For the following exercises, the vectors u and v are given. Find the vector projection w=projuv of...Problem 173E:
A methane molecule has a carbon atom situated at the origin and four hydrogen atoms located at...Problem 174E:
[T] Find the vectors that join the center of a clock to the hours 1:00,2:00, and 3:00. Assume the...Problem 175E:
Find the work done by force F=5,6,2 (measured in Newtons) that moves a particle form point P(3,1,0)...Problem 176E:
[T] A sled is pulled by exerting a force of 100N on a rope that makes an angle of 25 with the...Problem 177E:
[T] A father is pulling his son on a sled at an angle of 20 with the horizontal with a force of 25lb...Problem 178E:
[T] A car is towed using a force of 1600N . The rope used to pull the car makes an angle of 25 with...Problem 179E:
[T] A boat sails north aided by a wind blowing in a direction of N30E with a magnitude of 500lb ....Problem 180E:
Vector p=150,225,375 represents the price of certain models of bicycles sold by a bicycle shop....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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