Exercise 12.10. Using Properties of Dot Product Let a = (2, −3), b = (−5, 1), c = (4, −6), find each dot product: 1) (ab) c 4) ||a|| 2) a 2b . 3) a (b+c) 5) (ac) - (b · c) 6) 3 a b

Consider noncoplanar points A, B, C, and D. Using three points at a time such as A, B, and C, how many planes are determined by these points?

Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle. Exercises 34. 35

Note: Exercises preceded by an asterisk are of a more challenging nature. In Exercises 37 and 38, use the method of proof of Theorem 7.1.1 to justify each construction method. The perpendicular bisector method.