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A dimensional check in an equation can provide a quick check about the possible correctness of the equation. For example, if you are supposed to calculate a speed, the dimensions of the result MUST be of the form [distance] / [time] (or something that you can simplify to distance/time). If it doesn't, the formula is wrong. If it does, it MIGHT be correct.

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Q: What are the used of dimensional equation?

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A line, "living" in N-dimensional space, where N is the number of variables.

There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.

A cylinder does not have area, since it is a three dimensional object. Instead, it is usually described as having volume,

It can, but it can also determine a line in multi-dimensional (eg 3-d) space.

It depends on the equation that is being solved.

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Yes.

speed = distance / time

William Rowan Hamilton invented or discovered Linear equation. Which these equation describe mechanics in three dimensional space.

It is a linear equation in two dimensional space. Such an equation defines a line in 2-d

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yes

Since a triangle is two-dimensional, it cannot have volume.

The location of a point in 3-dimensional space.

An equation in 6 dimensional space!

Dimensional analysis simply ensures that two sides of an equation have the same dimensions. By "dimensions" I mean quantities like distance, pressure, force, time, electric charge, etc. For example, a distance can not equal a time. So, if the dimensions are wrong, the equation is wrong, but if the dimensions are right, the equation may be right or it may be wrong. Getting the dimensions right is only part of the task!

An ordered pair or coordinates of a point in 2-dimensional space.

3 dimensional geometry.3 dimensional geometry.3 dimensional geometry.3 dimensional geometry.

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