some questions about 3D environment

baby_1

Hello
I have some question that i confused to know them
1-what is difference between Vector and Line in 3D and 2D?
2-how can find the vertical vector on a surface or line?
3-how can find the angle between two vector or line only with their size?( i do it with Inner Product equation but without the Inner Product value how can do that

?)

Thanks

HallsofIvy

A vector has a specific length, a line extends infinitely. Also you can add vectors and multiply vectors by numbers. Lines have no "algebra".

What do you mean by "vertical"? Do you mean perpendicular? How you would find it depends on how you are given the surface or line. We can write a plane in three dimensions as Ax+ By+ Cz= D. In that case, any perpendicular vector is a multiplie of <A, B C>. If the "surface" is not a plane, perpendicular vectors will vary from point to point. A line, in two dimensions, written as y= ax+ b, has perpendicular vector <a, -1>.

You don't! Two vectors with the same lengths can have many different directions and so many different angles between them. The size of vectors is completely irrelevant to the angle between them.