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.
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