Name: _________________ Dot Products Reading Assignment: 1.3 Recommended exercises: 1 – 12 (some), 15, 17, 22, 26, 28 1) If a = 2i - 3j + 6k and b = 4i + 2j + 4k, find a b and the angle between a and b to the nearest degree. Find projab. 2) Find the interior angles of the triangle whose vertices are (1, 0, 2), (2,1, 1), and (1, 2, 2) . 3) Find three non-parallel non-zero vectors orthogonal to a above. Name: _________________ 4) Find z so that i + j + zk makes an angle of sixty degrees with b = 4i + 2j + 4k. Find q to minimize the angle between i + j + qk and b. 5) Find the angle between an edge of a cube and one of the long diagonals. 6) A vector originating at the origin makes an angle of 75 with the positive x-axis, and 35 with the positive y-axis. What angle does it make with the z-axis? Name: _________________ 7) Let a = (1,4) and b = (1,3) . Find projab and projba, then sketch all 4 vectors on the coordinate plane below. y 5 x -1 -5 5 8) Show that the vector v u u v bisects the angle between u and v .