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: Find (a) u.v (b) u.u (c) (b) (c)(d) (e) v(f) 2(g)(h)(i) (j) (d) (u.v)v (e) u.(3v) u= 3,4 v= 1,5 Problem 2E Problem 3E: Find (a) u.v (b) u.u (c) (b) (c)(d) (e) v(f) 2(g)(h)(i) (j) (d) (u.v)v (e) u.(3v) u= 6,4 v= 3,2 Problem 4E: Finding Dot Products In Exercises 18, find (a) u v, (b) u u, (c) ||u||2, (d) (u v) v, and (e) u... Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E: Finding the Angle Between Two Vectors In Exercises 11-18, find the angle between the vectors (a) in... Problem 15E: Finding the Angle Between Two Vector In Exercises 11-18, find the angle between the vectors (a) in... Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E: The vertices of a triangle are given. Determine whether the tringle is an acute triangle, an obtuse... Problem 27E Problem 28E Problem 29E: Finding Direction Angles In Exercises 31-36, find the direction cosines and angles of u and show... Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E: Finding Direction Angles In Exercises 31-36, find the direction cosines and angles of u and show... Problem 35E Problem 36E Problem 37E: (a) Find the projection of u onto v and (b) find the vector component of u orthogonal to v.... Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E: Finding the Projection of u onto v In Exercises 3542, (a) find the projection of u onto v, and (b)... Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E: When the projection of u onto v has the same magnitude as projection of v onto u, can you conclude... Problem 50E Problem 51E Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E: In exercise y=x2,y=x1/3 (a) Find all points of intersection of the graphs of the two equations (b)... Problem 68E: In exercise y=x3,y=x1/3 (a) Find all points of intersection of the graphs of the two equations (b)... Problem 69E Problem 70E Problem 71E Problem 72E: Use vectors to prove that parallelogram is a rectangle only and only if the diagonals are equal in... Problem 73E: Consider a regular tetrahedron with vertices 0,0,0, k,k,0 k,0,k, 0,k,k where k is a real positive... Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E format_list_bulleted