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If I wanted to write ##\hat{r}##in terms of ##\hat{x}##and ##\hat{y}##, is it ##\frac{\hat{x} + \hat{y}}{\sqrt{2}}## ?
Only if ##x=y\ge 0##.Arman777 said:If I wanted to write ##\hat{r}##in terms of ##\hat{x}##and ##\hat{y}##, is it ##\frac{\hat{x} + \hat{y}}{\sqrt{2}}## ?
... astnich said:Only if ##x=y\ge 0##.
In general ##\hat r= \frac{x\hat x + y\hat y} {\sqrt {x^2+y^2}}## for ##\sqrt {x^2+y^2}>0##.
Arman777 said:If I wanted to write ##\hat{r}##in terms of ##\hat{x}##and ##\hat{y}##, is it ##\frac{\hat{x} + \hat{y}}{\sqrt{2}}## ?
Arman777 said:I found an E field in the form of ##\vec{E} = C(\frac{1} {|\vec{r}|} - \frac{1} {|\vec{r} - \vec{d}|})\hat{r}## where C is a constant.
I need to transform this into x,y coordinates. So I wrote
##\vec{E} = C(\frac{1} {\sqrt{x^2 + y^2}} - \frac{1} {\sqrt{(x-d)^2 + (y-d)^2)}}) \frac{x\hat{i} + y\hat{j}}{\sqrt{x^2 + y^2}}##
Stephen Tashi said:What does the "##\hat{}##" in your notation signify? Is it only to indicate that variables are vectors? - or does it indicate vectors of length 1?
What is your definition of ##\hat{r}##?
my mistake ##\vec{d} = d\hat{i}##PeroK said:It looks like you have ##\vec d = (d, d)## there.
A radial vector in Cartesian form is a vector that is defined by its magnitude and direction in three-dimensional space. It is represented by three coordinates (x, y, z) and can be used to describe the position, velocity, or acceleration of an object.
A radial vector is a type of normal vector, but it is specifically oriented towards or away from a central point. This means that the magnitude and direction of a radial vector will change depending on the position of the object, while a normal vector remains constant.
To convert a radial vector to Cartesian form, you can use the following formula: x = r * cos(θ), y = r * sin(θ), z = z. Here, r is the magnitude of the vector, and θ is the angle between the vector and the x-axis. This will give you the x, y, and z coordinates of the vector in Cartesian form.
Yes, a radial vector can have negative values in Cartesian form. This occurs when the vector is pointing in the opposite direction of the positive axis. For example, a vector with coordinates (-3, 2, 0) would have a negative x-coordinate but positive y-coordinate.
Radial vectors are commonly used in physics to describe the motion of objects in three-dimensional space. They are important in fields such as mechanics, electromagnetism, and fluid dynamics, as they allow us to calculate the position, velocity, and acceleration of objects with respect to a central point or axis.