What is major difference in motion in a straight line and motion in a plane.

[Dr. Manoj]

1)I am confused why do we take vectors along y-axis and x-axis in motion on a plane? What's essence of learning vectors functions.
2)And in textbooks, they have given that motion in a straight line has 2 directions only. Hope many do motion on a plane has?
Please give me simple and detailed differences. With examples.

 

[Student100]

Not sure I completely understand what you're asking.

In one dimensional motion you basically have a number line. You can go forward or reverse. In two dimensions you have two degrees of freedom, you can go up/down, left/right, or some combination thereof.

Vectors in 2D are really two equations concatenated into one, the motion along the x-axis or the motion along the y axis. Each motion is independent of the other.

 

[sophiecentaur]

in textbooks, they have given that motion in a straight line has 2 directions only.

This is the basis of using vectors to describe motion (force and velocity etc. too). The principles of Resolving and Adding Vectors are what the elementary vector stuff is all about. If you are discussing motion on a plane then, if the 'one dimensional motion' is not in the direction of one of the cartesian axes, then there will be a component of the motion in the direction of both of the axes. Likewise, for motion in a 3D system, there can be components in the directions of all three axes. In all three cases, the motion is still the same as far as the object is concerned; using two/three dimensions and two/three vector components allows you to deal with motion that isn't in the direction of the original object's path. But if you can get away with one dimensional analysis then there's no point in getting into other dimensions.

 

[CWatters]

I'm not 100% sure I understand the question but...

1)I am confused why do we take vectors along y-axis and x-axis in motion on a plane?

Lots of reasons. Example: Splitting a vector into x and y components allows you to add vectors easily. Let's say you have two vectors (both on the same xy plane) and to want to add them together. You can do this by adding...

a)The x component of vector 1 to the x component of vector 2 to give the x component of the resulting vector.
b) The y component of vector 1 to the y component of vector 2 to give the y component of the resulting vector.

Are you familiar with the head to tail method of adding vectors? If you draw a diagram showing this you can see why the above method works.

2)And in textbooks, they have given that motion in a straight line has 2 directions only.

Think about a train on a straight railway line that goes North-South. The train can only go North or South. It cannot go East or West.

Hope [how] many do motion on a plane has?

The answer is infinite. A ship can go in any direction on a lake.

 

[sophiecentaur]

given that motion in a straight line has 2 directions only.

I have read this again and re-parsed the question. The answer could be that, to stay on a straight line whilst you are moving, you can only be going forwards or backwards. A number (speed) and a sign (+=forwards and -=backwards) is one dimensional information and can describe all possible velocities / displacements / accelerations etc. etc.
You need more information if you want to describe any motion that isn't on the line - for instance, how far either side and how far up or down requires two extra pieces of information. You have to go from just an x to x,y and z. it is usual but not absolutely essential to have the three axes at right angles and there are other co ordinate systems than cartesian (e.g. Polar) and vector calculations can use them.

Is any of this stuff making sense to you, Dr Manoj?

 

[Dr. Manoj]

I have read this again and re-parsed the question. The answer could be that, to stay on a straight line whilst you are moving, you can only be going forwards or backwards. A number (speed) and a sign (+=forwards and -=backwards) is one dimensional information and can describe all possible velocities / displacements / accelerations etc. etc.
You need more information if you want to describe any motion that isn't on the line - for instance, how far either side and how far up or down requires two extra pieces of information. You have to go from just an x to x,y and z. it is usual but not absolutely essential to have the three axes at right angles and there are other co ordinate systems than cartesian (e.g. Polar) and vector calculations can use them.

Is any of this stuff making sense to you, Dr Manoj?

Thank you, I got it. Another question is that, do we need to consider dot product and cross product to mention position of a particle?

 

[jtbell]

do we need to consider dot product and cross product to mention position of a particle?

Dot product and cross product of what?