need help with vectors...?

Question

i really dont understand what vectors are. how is a vector different from a line? please fully describe a vector. thank you

Answer 1

A vector is a quantity that has magnitude and direction. It can be represented as a line, but you need an arrow to indicate the direction. The length of the line represents the magnitude. Note that the line is not the vector itself, just the graphical representation of a vector. For example, a car's velocity is a vector: the magnitude is its speed. You can represent a car's velocity as a line with an arrow at the end pointing to the direction of travel (e.g. on a map), and the length of the line indicating the speed. You could include a scale so that the speed could be indicated accurately. However, the car's velocity is not a line, but it is a vector.

Answer 2

You draw a vector as a 'kind of' a line to help you visualize what's going on with them. But a line is a collection of points, a vector is not.

A vector is used to describe something that has both a magnitude -and- a direction. If you say, "I rode my bike for 2 km.' that tells me how far you rode, but it tells me nothing abouyt where you went because I don't have a clue which way you went. If Joe and Sam are both pushing on a car, but the car isn't moving, it may be because they're pushing in opposite directions and the 'net' force on the car is zero.

Another (and, later on, much more useful) way to think about vectors is that a vector is an 'ordered pair' of numbers that represent the coordinates of a point in the (x, y) plane. If you connect this point with the origin, the line segment you just drew has both a magnitude (it's length) and a direction (which way it points). It's also possible to have an 'ordered triple' of numbers which describes a point (and a vector) in 3-dimensional space.

Vectors are used all over the place in science, physics, engineering, navigation, and a lot of other things. Pay close attention to them and learn them well. Especially learn how to add, subtract, multiply, and divide vectors. If you learn those cold, Physics will be a piece of cake ☺

Doug

Answer 3

A line is nothing more than a connection between two points. A vector, on the other hand, has two main components: a magnitude and a direction. Vectors can describe things like velocity for example. A velocity vector not only shows which direction the object is moving (whichever way the arrow points) but it shows the magnitude of the velocity (how fast it is moving). Normally, the longer the arrow used to represent the vector the greater its magnitude is.

Answer 4

Vectors too are lines, but they also have a direction as well as magnitude.

If you are asked where is east or west, you point your hand in that direction. Here you are drawing a vector in space. (This illustrates only the direction aspect of the vector).

If you are pushing a table in a direction, the magnitude aspect too come into picture. The force with which you push can be represented by a vector whose direction (arrow direction of the vector) gives the direction of push and magnitude (length of the vector) gives the magnitude of push (in units like Kilogram force).

Now you know that not just the magnitude of this push is important, but also the direction. Because, if another person comes to help you push the table his vector should be obviously in the direction of your vector, else it will not help your cause.