Scalar Product Tests (HL only)

a. b=a_1b_1+a_2b_2+a_3b_3, a. a=| a|2 For nonzero vectors, costheta= a. b| a|| b|, where 0 <= theta <= pi. A negative scalar product gives an obtuse vector angle. a b a. b=0, for nonzero vectors. Parallel vectors satisfy a=k b, equivalently | a. b|=| a|| b|. (k a). b=k(a. b), a. (b+ c)= a. b+ a. c. Example For a=(1,2,-1), b=(3,-1,1), a. b=3-2-1=0; the nonzero vectors are perpendicular.