xsever said:
I'm guessing that you mean [itex]\vec{A}=2\hat{x}-5\hat{y}+3\hat{z}[/itex] and that the problem is to express this vector in terms of the spherical basis vectors at the point [itex](x,y,z)=(-2,3,1)[/itex]. Does this sound right?xsever said:
The formula for converting Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ) with a point is:
r = √(x² + y² + z²)
θ = arctan(y/x)
φ = arccos(z/r)
Cartesian coordinates are a system for representing points in three-dimensional space using three perpendicular axes (x, y, z). In contrast, spherical coordinates use a radial distance (r), an azimuthal angle (θ), and a polar angle (φ) to describe points in three-dimensional space.
To convert from spherical coordinates (r, θ, φ) back to Cartesian coordinates (x, y, z), use the following formulas:
x = r sin(φ) cos(θ)
y = r sin(φ) sin(θ)
z = r cos(φ)
Converting between Cartesian and spherical coordinates is commonly used in fields such as mathematics, physics, and engineering. It can be used to describe the position of objects in space, map out geographic locations, and solve geometric problems involving three-dimensional shapes.
While spherical coordinates are useful for describing points in three-dimensional space, they are not always the most convenient or accurate system to use. For instance, they can be difficult to visualize and work with in certain situations, and may be less precise for measuring distances compared to Cartesian coordinates.