Let and be differentiable vector-valued functions such that for all
MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Let r(t) and s(t) be differentiable vector-valued functions such that r(t)⋅s(t)=0 for all t. Which of the following must hold for every t?
(a) r′(t)⋅s(t)=0
(b) r′(t)⋅s(t)+r(t)⋅s′(t)=0
(c) r′(t)⋅s(t)−r(t)⋅s′(t)=0
(d) r′(t)⋅s′(t)=0