prove that projuvprojuv 0 also written as projection of v

prove that proju(v-proju(v)) = 0 also written as : projection of ( v- projection of v ont u) onto u = 0

please explain

thanks

Solution

answer =either v is parallel to u or v is perpendicular to u

EXPLANATION . projection of v on u is v cosA where A is the angle between u and v. v- projection of v on u=v-vcosA=v(1-cosA) . Projection ofv(1-cosA) on u=v(1-cosA)cosA=0

Either cosA=0 or 1-cosA=0 hence A=0 or A=90degree.