The word dimension has special meaning in physics. It is used to denote the nature of a physical quantity. Whether a distance is measured in any units, metres, miles or even light year. It is always distance and its dimension is length.
The symbols L, M and T are the symbols usually used to specify the dimensions of length, mass and time respectively. The dimension of any quantity can always be expressed as some combination of the fundamental quantities, such as mass, length and time.
The dimension of velocity are written as L/T and the dimensions of area are L 2.
In any equation the dimension of physical quantity must be same on both sides of equation. The dimensional tables attached to the various quantities may treated like algebraic quantities and may be combined. cancelled etc just as if they were factors in the equation.
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