Prove that cylindrical coordinate
system is orthogonal.
.
Answers
Explanation:
A simple method for generating orthogonal coordinates systems in two dimensions is by a conformal mapping of a standard two-dimensional grid of Cartesian coordinates (x, y). A complex number z = x + iy can be formed from the real coordinates x and y, where i represents the imaginary unit.
Concept introduction:
Orthogonal means the points are at right angle. Cylindrical coordinates are orthogonal.
Explanation:
Given that, cylindrical coordinates are orthogonal.
We have to find, prove of cylindrical coordinates are orthogonal.
According to the question,
If we draw tangent at any coordinate then we will find that cylindrical coordinate are orthogonal. Since dx, dy, and dz are all lengths in the Cartesian coordinate system, it is length-based and orthogonal in the cylindrical coordinate system. However, some differential changes, such d, d, do not depend on length in other curved coordinate systems, including cylindrical and spherical ones.
Final Answer:
Cylindrical coordinate are orthogonal.
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