Problem 1E Problem 2E Problem 3E: What is the magnitude of the cross product of two parallel vectors? Problem 4E Problem 5E: Explain how to use a determinant to compute u v. Problem 6E: Explain how to find the torque produced by a force using cross products. Problem 7E: Cross products from the definition Find the cross product u v in each figure. 7. Problem 8E: Cross products from the definition Find the cross product u v in each figure. 8. Problem 9E: Cross products from the definition Sketch the following vectors u and v. Then compute |u v| and... Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E: Coordinate unit vectors Compute the following cross products. Then make a sketch showing the two... Problem 16E Problem 17E Problem 18E: Coordinate unit vectors Compute the following cross products. Then make a sketch showing the two... Problem 19E Problem 20E Problem 21E: Area of a parallelogram Find the area of the parallelogram that has two adjacent sides u and v. 21.... Problem 22E: Area of a parallelogram Find the area of the parallelogram that has two adjacent sides u and v. 22.... Problem 23E: Area of a parallelogram Find the area of the parallelogram that has two adjacent sides u and v. 23.... Problem 24E: Area of a parallelogram Find the area of the parallelogram that has two adjacent sides u and v. 24.... Problem 25E: Area of a triangle For the given points A, B, and C, find the area of the triangle with vertices A,... Problem 26E Problem 27E: Area of a triangle For the given points A, B, and C, find the area of the triangle with vertices A,... Problem 28E: Area of a triangle For the given points A, B, and C, find the area of the triangle with vertices A,... Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E: Orthogonal vectors Find a vector orthogonal to the given vectors. 35. 0, 1, 2and 2, 0, 3 Problem 36E: Orthogonal vectors Find a vector orthogonal to the given vectors. 36. 1, 2, 3and 2, 4, 1 Problem 37E: Orthogonal vectors Find a vector orthogonal to the given vectors. 37. 8, 0, 4and 8, 2, 1 Problem 38E Problem 39E Problem 40E Problem 41E: Computing torque Answer the following questions about torque. 41. Let r=OP=i+j+k. A force F = 20, 0,... Problem 42E: Computing torque Answer the following questions about torque. 42. Let r=OP=ij+2k. A force F = 10,... Problem 43E: Computing torque Answer the following questions about torque. 43. Let r=OP=10i. Which is greater (in... Problem 44E: Computing torque Answer the following questions about torque. 44. A pump handle has a pivot at (0,... Problem 45E: Force on a moving charge Answer the following questions about force on a moving charge. 45. A... Problem 46E Problem 47E Problem 48E: Force on a moving charge Answer the following questions about force on a moving charge. 48. A proton... Problem 49E Problem 50E: Collinear points Use cross products to determine whether the points A, B, and C are collinear. 50.... Problem 51E: Collinear points Use cross products to determine whether the points A, B, and C are collinear. 51.... Problem 52E: Finding an unknown Find the value of a such that a, a, 2 1, a, 3 = 2, 4, 2. Problem 53E Problem 54E: Areas of triangles Find the area of the following triangles T. 54. The sides of T are u = 0, 6, 0, v... Problem 55E: Areas of triangles Find the area of the following triangles T. 55. The sides of T are u = 3, 3, 3,v... Problem 56E Problem 57E: Areas of triangles Find the area of the following triangles T. 57. The vertices of T are O(0, 0, 0),... Problem 58E Problem 59E Problem 60E Problem 61E Problem 62E: Express u, v, and w in terms of their components and show that u(v w) equals the determinant... Problem 63E Problem 64E Problem 65E Problem 66E: Arm torque A horizontally outstretched arm supports a weight of 20 lb in a hand (see figure). If the... Problem 67E Problem 68E: Three proofs Prove that u u = 0 in three ways. a. Use the definition of the cross product. b. Use... Problem 69E: Associative property Prove in two ways that for scalars a and b, (au) (bv) = ab(u v). Use the... Problem 70E Problem 71E Problem 72E Problem 73E: Identities Prove the following identities. Assume that u, v, w, and x are nonzero vectors in 3. 73.... Problem 74E Problem 75E: Cross product equations Suppose u and v are known nonzero vectors in 3. a. Prove that the equation u... format_list_bulleted