1 Preparation For Calculus 2 Limits And Their Properties 3 Differentiation 4 Applications Of Differentiation 5 Integration 6 Differential Equations 7 Applications Of Integration 8 Integration Techniques, L’ho?pital’s Rule, And Improper Integrals 9 Infinite Series 10 Conics, Parametric Equations, And Polar Coordinates 11 Vectors And The Geometry Of Space 12 Vector-Valued Functions 13 Functions Of Several Variables 14 Multiple Integration 15 Vector Analysis expand_more
11.1 Vectors In The Plane 11.2 Space Coordinates And Vectors In Space 11.3 The Dot Product Of Two Vectors 11.4 The Cross Product Of Two Vectors In Space 11.5 Lines And Planes In Space 11.6 Surfaces In Space 11.7 Cylindrical And Spherical Coordinates Chapter Questions expand_more
Problem 1E: Cross Product of Unit Vectors In Exercises 3-6, find the cross product of the unit vectors and... Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E: Finding Cross Products In Exercises 7-10, find (a) uv, (b) vu, and (c) vv. u=2i+4jv=3i+2j+5k Problem 8E: Finding Cross Products In Exercises 7-10, find (a) uv, (b) vu, and (c) vv. u=3i+5kv=2i+3j2k Problem 9E Problem 10E Problem 11E Problem 12E: Finding a Cross Product In Exercises 1116, find u x v and show that it is orthogonal to both u and... Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E: Finding a Unit Vector In Exercises 15-18. Find a unit vector that is orthogonal to both u and v.... Problem 19E: Finding a Unit Vector In Exercises 15-18. Find a unit vector that is orthogonal to both u and v.... Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E: Area In Exercises 23 and 24, verify that the points are the vertices of a parallelogram, and find... Problem 26E: Area In Exercises 23 and 24, verify that the points are the vertices of a parallelogram, and find... Problem 27E: Area In Exercises 25 and 26, find the area of the triangle with the given vertices. (Hint: 12uv is... Problem 28E Problem 29E: Torque The brakes on a bicycle are applied using a downward force of 20 pounds on the pedal when the... Problem 30E Problem 31E Problem 32E Problem 33E: Finding a Triple Scalar Product In Exercises 31-34, find u(vw) u=iv=jw=k Problem 34E: Finding a Triple Scalar Product In Exercises 31-34, find u(vw) u=1,1,1,v=2,1,0w=0,0,1 Problem 35E Problem 36E Problem 37E: Volume In Exercises 35 and 36. use the triple scalar product to find the volume of the... Problem 38E Problem 39E: Volume In Exercises 37 and 38, find the volume of the parallelepiped with the given vertices.... Problem 40E: Volume In Exercises 37 and 38, find the volume of the parallelepiped with the given vertices.... Problem 41E Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E: True or False? In Exercises 43-46, determine whether the statement is true or false. If it is false,... Problem 50E: True or False? In Exercises 43-46, determine whether the statement is true or false. If it is false,... Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E: Proof In Exercises 47-52. prove the property of the cross product. uv=0 if and only if u and v are... Problem 57E Problem 58E: Proof Prove that u(vw)=(uw)v(uv)w Problem 59E format_list_bulleted