Need help with vectors
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Need help with vectors
I'm taking physics right now and cannot figure out these things called vectors. Adding vectors, subtracting vectors, multiplying vectors, dividing vectors, polar and rectangular coordinates are areas that i need help in.... Any assistance will be much appreaciated...
"Bother"
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Sai - Posts: 451
- Joined: Mon Jan 24, 2005 10:00 am
- Location: Michigan
It would help if you were more specific. For example, if you posted some problems that were giving you difficulty it would be for us to explain.
To begin with however, here are a few basic definitions:
Rectangular coordinates: these are the simple (x,y) cartesian coordinates that you should already be familiar with. These can be extended to 3 or more dimensions simply by adding an extra dimension that is orthogonal to the others.
http://mathworld.wolfram.com/CartesianCoordinates.html
Polar coordinates: Instead of measuring the position in terms of grid coordinates (x,y), we can also measure position in terms of the distance r from the origin and angle theta from some baseline.
http://mathworld.wolfram.com/PolarCoordinates.html
As for your other questions:
1)Vector addition-> Given a vector a=(x1,y1,z1) and another b=(x2,y2,z2), summation is carried out in an elementwise fashion. a+b=(x1+x2,y1+y2,z1+z2).
2)Vector subtraction-> This is the same as addition.
3)Vector multiplication-> There is a scalar (dot) product and a vector (cross) product.
http://mathworld.wolfram.com/DotProduct.html
http://mathworld.wolfram.com/CrossProduct.html
Multiplication by a scalar is done on an elementwise basis i.e. multiply each element in the vector by the scalar in question
4)Vector division->Division by a scalar is done on an elementwise basis, so each element must be divided by the scalar. Vectors themselves cannot be divided into each other.
To begin with however, here are a few basic definitions:
Rectangular coordinates: these are the simple (x,y) cartesian coordinates that you should already be familiar with. These can be extended to 3 or more dimensions simply by adding an extra dimension that is orthogonal to the others.
http://mathworld.wolfram.com/CartesianCoordinates.html
Polar coordinates: Instead of measuring the position in terms of grid coordinates (x,y), we can also measure position in terms of the distance r from the origin and angle theta from some baseline.
http://mathworld.wolfram.com/PolarCoordinates.html
As for your other questions:
1)Vector addition-> Given a vector a=(x1,y1,z1) and another b=(x2,y2,z2), summation is carried out in an elementwise fashion. a+b=(x1+x2,y1+y2,z1+z2).
2)Vector subtraction-> This is the same as addition.
3)Vector multiplication-> There is a scalar (dot) product and a vector (cross) product.
http://mathworld.wolfram.com/DotProduct.html
http://mathworld.wolfram.com/CrossProduct.html
Multiplication by a scalar is done on an elementwise basis i.e. multiply each element in the vector by the scalar in question
4)Vector division->Division by a scalar is done on an elementwise basis, so each element must be divided by the scalar. Vectors themselves cannot be divided into each other.
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov
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Technomancer - Posts: 2379
- Joined: Fri Jun 13, 2003 11:47 am
- Location: Tralfamadore
I just took this test and got a "c" im mad at myself... I understood the information but I got sick the day before the test and stayed sick for three days.. then it was the weekend and I had to take the test monday... I didn't have time to study... oh well!!
anwyays for vectors the best way to figure them out is to draw them out!
so if your problem says you need to find the displacement for a person who walked 5o meters/s north and then walked walked 100 meters/s east map it out
^-100m->
I
5
0
I okay there is your vector... what your looking for is the line that would connect it and make it a triangle... and in triangles everyone knows..
A squared plus B squared equals C squared so plug it in and you should get something like 111.8
so thats the first part of your answer!
now you need to find your angle to do that you need to use your trig functions! that would be your sine cosine and tangent...
well use tangent wich is
tangent= opp/adj
so plug it in
tangent=100/50
your tan should end up equaling something like 2.. actually it should equal 2 exactly!!
now take tan-1 of two
this will give you 63.43 degrees
so your final answer is
111.8meters/s 63.43 degrees East of North
Welll I hope that helps...
anwyays for vectors the best way to figure them out is to draw them out!
so if your problem says you need to find the displacement for a person who walked 5o meters/s north and then walked walked 100 meters/s east map it out
^-100m->
I
5
0
I okay there is your vector... what your looking for is the line that would connect it and make it a triangle... and in triangles everyone knows..
A squared plus B squared equals C squared so plug it in and you should get something like 111.8
so thats the first part of your answer!
now you need to find your angle to do that you need to use your trig functions! that would be your sine cosine and tangent...
well use tangent wich is
tangent= opp/adj
so plug it in
tangent=100/50
your tan should end up equaling something like 2.. actually it should equal 2 exactly!!
now take tan-1 of two
this will give you 63.43 degrees
so your final answer is
111.8meters/s 63.43 degrees East of North
Welll I hope that helps...
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Kuro-Mizu - Posts: 578
- Joined: Fri Dec 17, 2004 5:28 pm
- Location: Near insanity!
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