Vector function satisfies for all real

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Vector function

r(t)

satisfies

|r(t)| = 5

for all real

t

. Determine

r(t)\cdot r'(t)

for every

t

and briefly justify your result.