vectors please help?

Question

what can you infer (a) projection of u onto v equals u
(b) projection of u onto v equals zero. what can be said about vectors u and v under each condition

Answer 1

u and v are parallel. a projection of u onto v, is basically taking the component of u that is in the v direction. so if the projection of u onto v is u, then the whole vector is in the v direction, so they are parallel.

if the projection is 0, then u and v are perpendicular. cuz ya same reason. if u and v are perpendicular, then there is no component of u in the v direction, so the projection would be 0.

hope that helps.

Answer 2

Given vectors u and v, what can you infer?

(a) projection of u onto v equals u
u and v are parallel

(b) projection of u onto v equals zero
u and v are perpendicular

Answer 3

a) u and v are parallel
b) u and v are perpendicular

Answer 4

nice question