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Math 223 1. 2. a. Vector (cross) product Name_____________________ Let || a || 8, || b || 5 and a b 30 . Find || a b ||. Let v 2i 3 j k and w i 2 j . Find v w b. Find || v w || c. Show that v w is perpendicular to both v and w . d. Find the area of the parallelogram built on vectors 3. Find i j i j . v and w . 4. Find a unit vector that is perpendicular to both d i k . 5. Let c i j and A(2, 2,1), B3, 1, 2, C 3, 1,1, D4, 3, 4 . a. Find the area of the triangle determined by the points A, B, C. b. Find the volume of the parallelepiped determined by A, B, C, D. c. Find a vector that is perpendicular to the plane containing points A, and C. d. Find the distance from the point D to the plane containing points A, and B, C. B,