Vector Projection

[taha2002]

Show using diagrams...
(a) Is it possible for the projection of vector a onto vector b to be equal to 0?
(b) Is it possible for the projection of vector a onto vector b to be undefined?
(c) Is it possible for the projection of vector a onto vector b to be equal to the projection of vector b onto vector a?
(d) Explain why a↓c = a↓(b↓c). *a, b, and c are vectors.*

My answers:
(a) Yes. If vector a and vector b are perpendicular to each other. (Not sure)
(b) Yes. If the magnitude of vector b is 0. (Not sure)
(c) Yes. If vector a and vector b are on the same line. – If that is the case, do the two vectors then have to have the same magnitude and direction too?] (Not sure)
(d) I can show this without a problem.

Thank for your help.

 

[Dr.Peterson]

Show using diagrams...
(a) Is it possible for the projection of vector a onto vector b to be equal to 0?
(b) Is it possible for the projection of vector a onto vector b to be undefined?
(c) Is it possible for the projection of vector a onto vector b to be equal to the projection of vector b onto vector a?
(d) Explain why a↓c = a↓(b↓c). *a, b, and c are vectors.*

My answers:
(a) Yes. If vector a and vector b are perpendicular to each other. (Not sure)
(b) Yes. If the magnitude of vector b is 0. (Not sure)
(c) Yes. If vector a and vector b are on the same line. – If that is the case, do the two vectors then have to have the same magnitude and direction too?] (Not sure)
(d) I can show this without a problem.

Thank for your help.

If you were told to show these facts using diagrams ... then do so, and show us your diagrams. They may convince you where you are unsure. (On the other hand, a diagram is not a proof, and could miss special cases, or could be a special case.)

I'm not sure I could be fully convinced by a diagram for (b), since it's hard to show something that's undefined, but that may depend on how you were taught to diagram it. I might prefer using the definition or a formula for that.

It appears that a↓c is your notation for vector projection of a on c? I don't think I've ever seen it before.