The dot product is the of 2 vectors. The result is a The dot product for any two vectors is defined as the product of their magnitudes multiplied by the cosine of th angle between the two vectors when the two vectors are placed in a tail-to-tail position. Eg.1: If a = %(and b = ) , find a. % if the angle between them is 75 and 130 .+( When 6 is acute, When 0 is 909 therefore a and b are When 6 is obtuse,_, a=2 _, b _; Eg.2: If the vectors 21+ , 2, and 4a- 3) are perpendicular, and , determine the angle (to the nearest _. tenth of a degree) between the nonzero vectors a and B . The Dot Product of Algebraic Vectors In R2 , if a = [a, , a,] and b = [b, , b, then In R3 , if a = [a, , a2 , a3] and b = [b, , b, , b, then Proof in textbook p.379 Eg.1: If a = [3,2] and b = [4, - 1 then; a) Determine a b Find the angle between a and b