Give a brief description of the symmetric equation of a line.

Question:

Give a brief description of the symmetric equation of a line.

Symmetric Equation:

A line can be defined by two geometric elements: a point and its direction.

With these two elements, we can obtain various equations: such as parametric and symmetric

Answer and Explanation:

A symmetric equation of a line can be obtained from a point {eq}P(a,b,c) {/eq} an a direction of the line {eq}v = \left\langle {d,e,f} \right\rangle {/eq}, with these two elements we can write the equation: {eq}\frac{{x - a}}{d} = \frac{{y - b}}{e} = \frac{{z - c}}{f}. {/eq}


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How to Write a Linear Equation

from Math 101: College Algebra

Chapter 1 / Lesson 7
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