Question

If my teacher gives me two vectors and asks what do these mean geometrically... What would be an ideal answer?

Answer 1

The one (s)he's looking for.

Just kidding. Assuming two dimensional space, you can talk about whether or not they're parallel, what angle they intersect at if they're not, if they're perpindicular, what their slope is (depending on how he defines them), etc.

Answer 2

Wait, is your teacher asking for what they mean geometrically or for the geometric mean?

Answer 3

Vectors, geometrically, have length and direction, and can be thought of as directed line segments. In keeping with the need to conceive of vectors as generally as possible, this allows for vectors to "move" or "slide". That means that they don't always have to have their beginning point at the point (0, 0) which is the origin. You can have a vector parallel to another vector, and as long as it is pointed in the same direction and is the same length, they are considered equal.

Answer 4

No like my teacher is teaching us about projections and he might ask us like explain what it means geometrically something like that?

Answer 5

Ah, that's completely different than what you originally asked. I'm rusty on projections so I'm going to have to defer to someone else.

Answer 6

So, in short, they are directed line segments. They have length and direction.

Answer 7

yes okay

Answer 8

Algebraically, they can be as abstract as you want to make them and are a large part of linear and abstract algebra.

Answer 9

@tcarroll010...she's asking about projections.

Answer 10

It looked like her question was about vectors and what would she say if a teacher asked her regarding a geometric meaning.

Answer 11

I'm not sure He just said be able to describe what projection means geometrically..?

Answer 12

@butterflyprincess, I think your best bet may be to close this question and open a new one that specifically mentions projections.

Answer 13

ohok

Answer 14

Picture of a vector projection:This is when you take the end of the one vector and draw a perpendicular segment to the other vector. The area from the vertex to the intersection is the projection.