Problem 1E: Find the cross product a b and verify that it is orthogonal to both a and b. 1. a = 2, 3, 0, b = 1,... Problem 2E Problem 3E Problem 4E Problem 5E Problem 6E: Find the cross product a b and verify that it is orthogonal to both a and b. 6. a = ti + cos tj +... Problem 7E Problem 8E: If a = i 2k and b = j + k, find a b. Sketch a, b, and a b has vectors starting at the origin. Problem 9E: Find the vector, not with determinants, but by using properties of cross products. 9. (i j) k Problem 10E: Find the vector, not with determinants, but by using properties of cross products. 10. k (i 2j) Problem 11E: Find the vector, not with determinants, but by using properties of cross products. 11. (j k) (k ... Problem 12E: Find the vector, not with determinants, but by using properties of cross products. 12. (i + j) (i ... Problem 13E: State whether each expression is meaningful. If not, explain why. If so, state whether it is a... Problem 14E: Find |u v| and determine whether u v is directed into the page or out of the page. 14. Problem 15E: Find |u v| and determine whether u v is directed into the page or out of the page. 15. Problem 16E Problem 17E: If a = 2, 1, 3 and b = 4, 2, 1, find a b and b a. Problem 18E Problem 19E: Find two unit vectors orthogonal to both 3, 2, 1 and 1, 1, 0. Problem 20E: Find two unit vectors orthogonal to both j k and i + j. Problem 21E Problem 22E Problem 23E Problem 24E: Prove the property of cross products (Theorem 11). 24. Property 2: (ca) b = c(a b) = a (cb) Problem 25E Problem 26E Problem 27E: Find the area of the parallelogram with vertices A(3, 0), B(1, 3). C(5, 2), and D(3. 1). Problem 28E: Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3). R(7, 5, 8), and S(5,2, 7). Problem 29E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and (b) find the... Problem 30E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and (b) find the... Problem 31E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and (b) find the... Problem 32E Problem 33E: Find the volume of the parallelepiped determined by the vectors a, b. and c. 33. a = 1, 2, 3), b =... Problem 34E: Find the volume of the parallelepiped determined by the vectors a, b. and c. 34. a = i + j , b = j +... Problem 35E: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. 35. P(2, 1, 0), Q(2. 3.... Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E: Let v = 5j and let u be a vector with length 3 that starts at the origin and rotates in the... Problem 43E Problem 44E Problem 45E: (a) Let P be a point not on the line L that passes through the points Q and R. Show that the... Problem 47E Problem 48E Problem 49E: Prove that (a b) (a + b) = 2(a b). Problem 50E Problem 51E: Use Exercise 50 to prove that a (b c) + b (c a) + c (a b) = 0 Problem 52E: Prove that (ab)(cd)=|acbcadbd| Problem 53E Problem 54E: If v1, v2, and v3 are noncoplanar vectors, let k1=v2v3v1(v2v3) k2=v3v1v1(v2v3) k3=v1v2v1(v2v3)... format_list_bulleted