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Definition: A way of describing a line L is to eliminate the parameter t from the equations x = x_0 + at, y = y_0 + bt, and z = z_0 + ct. If none of a, b, c is 0, we can solve each of these equations for t, equate the results and obtain (x-x_0)/a = (y-y_0)/b = (z-z_0)/c. These equations are called symmetric equations of L.
Source: Multivariable Calculus, 7th edition by James Stewart