Problem 1E Problem 2E Problem 3E: 17 Find the cross product ab and verify that it is orthogonal to both a and b. a=2j4k, b=i+3j+k Problem 4E: 17 Find the cross product ab and verify that it is orthogonal to both a and b. a=3i+3j3k, b=3i3j+3k Problem 5E Problem 6E Problem 7E Problem 8E: If a=i2k and b=j+k, find ab. Sketch a, b, and ab. as vectors starting at the origin. Problem 9E Problem 10E: 912 Find the vector, not with determinants, but by using properties of cross products. k(i2j) Problem 11E: 912 Find the vector, not with determinants, but by using properties of cross products. (jk)(ki) Problem 12E: 912 Find the vector, not with determinants, but by using properties of cross products. (i+j)(ij) Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E: If a=1,0,1,b=2,1,1, and c=0,1,3, show that a(bc)(ab)c Problem 19E: Find two unit vectors orthogonal to both 3,2,1 and 1,1,0. Problem 20E Problem 21E Problem 22E Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E 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: 2932 a Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and b find the... Problem 30E: 2932 a Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and b find the... Problem 31E: 2932 a Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and b find the... Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E: A wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. A force is... Problem 42E Problem 43E Problem 44E: a Find all vectors v such that 1,2,1v=3,1,5 b Explain why there is no vector v such that... Problem 45E Problem 46E: a Let P be a point not on the plane that passes through the points Q, R, and S. Show that the... Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E: Suppose that a0. a If ab=ac, does it follow that b=c? b If ab=ac, does it follow that b=c? c If... Problem 54E: If v1, v2, and v3 are noncoplanar vectors, let k1=v2v3v1(v2v3)k2=v3v1v1(v2v3) k3=v1v2v1(v2v3) These... format_list_bulleted