MATH 210 Study Guide - Final Guide: Cross Product, Horse Length, Ellipse
Document Summary
Problem 1 solution: a triangle has vertices at the points. A = (1, 1, 1), b = (1, 3, 4), and c = (2, 1, 3) (a) find the cosine of the angle between the vectors ab and ac. (b) find an equation of the plane containing the triangle. Solution: (a) by de nition, the angle between two vectors ab and ac is: cos = The vectors are ab = h0, 4, 3i and ac = h1, 2, 2i. Thus, the cosine of the angle between them is: cos = ||h0, 4, 3i|| ||h1, 2, 1i|| p02 + ( 4)2 + 32p12 + ( 2)2 + 22 (0)(1) + ( 4)( 2) + (3)(2) 15 (b) a vector perpendicular to the plane is the cross product of ab and ac which both lie in the plane. N = [( 4)(2) (3)( 2)] [(0)(2) (3)(1)] + k [(0)( 2) ( 4)(1)] N = 2 + 3 + 4 k.
