Where does it point?
no where.... or everywhere... depending on how you want to look at it. Also, what's its magnitude? hasn't one of those either... so why is it a vector? because we've defined it that way. just like the zero in numbers, its a special little bugger.
Hehe, I can put a little trick question here,
When we add two vectors, we know that the tail of one and the head of the other together form the resultant vector.
Lets take the zero vector, if it points nowhere then what is the addition of a non-zero vector and the zero vector pointing to? If it points everywhere, then why is the addition of a non-zero vector and a zero vector points in the direction where the non-zero vector pointed?
It doesn't matter which way it points. Choose any direction - when you add the vector it will have the same resultant direction.
Gale is actually right, the point is whether my question is really tricky?
I don't see what's the catch here.The 0 vector is just an ordinary element of the vector space.
The zero vector is that (unique) element 0, for which 0+x=x for all vectors x in your vector space. Don't worry about where it points. Since its magnitude is zero, it's direction is meaningless concept (just like the argument for 0 in the complex plane).
the reason this topic seems tricky to beginners, is they forget to ask for the definition of the crucial concept, here "direction", before beginning to run with the ball.
instead they go off guided by misleading but popular phrases, like: "every vector has a magnitude and a direction".
this is the basic difference between learning mathematics and just trotting along in the peanut gallery. of course this may all be a joke, but the phenomenon mentioned here seems very real to me, from my perspective as a (would be) teacher.
i hated that phrase that appears in text books beloved of so many calc courses (in the US sense): a vector is something that has magnitude and direction. So crap. how about "a number is something you can add to something else"? That's just as bad but they wouldn't dare use that at all.
Anyway, the idea that vectors even have directionm at all is dubious, though often usseful. not always though. vector quantities in the physics/mechanics usage of the term may be usefully said to have directions, but a vector quantity with no magnitude isn't acting in any direction really.
A vector can be simply thought of as drawing a line(say in a paint program). The length of the line denotes its magnitude and the direction in which i drag my mouse becomes the direction of that vector. Now try to draw a line with magnitude zero and the direction of it becomes clear
A vector is something abstract.It is an element of a set.Therefore i could use any graphical symbol to "picture" it on the paper or in my mind.Even a circle or a sphere.
I lie here, mourning over the days i lived as a dead man. I could never understand what love was, it was too abstract for me. Leela, if you are reading this, then i would like to tell you, now i know. Now i know that love is you and now i know why you left me. Forgive me if you can. Let my deathbed be a reminder for those, who live a dead life. They should know, they may never get a second chance. -- Amit
Not to be sounding too poetical here, but various abstract things are understood in a completely different way by different individuals. Just pointing out how you understood could help the other person who is struggling with it.
So the zero vector points towards love?
Yes, us males always carry these "zero vectors" inside us and give them to every good looking dame that passes by. Since it is of zero magnitude, there are abundant of it with us that we distribute. Its just them females, who keep attaching some magnitude to it, oh dear! :surprised
WOW... how bout you boys stick to math eh.
My love vector has a magnitude though :rofl:
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