Equations of Lines and Normal Vectors | Massachusetts Institute of Technology - Edubirdie

University:
Massachusetts Institute of Technology
Course:
18.089 | Review of Mathematics
Academic year:

2022
Views:

155

Pages:

1
Author:

Sporkz

Equations of lines and normal vectors We use numbers now, but you can substitute any letter for each variable. If you have ax plus by plus c, the same story applies. By the same reasoning, if the line ax + by + c = 0, then the vector (a, b) is perpendicular to the line. That’s it. Can zero be replaced with any number? Or, can it be like ax plus by plus c equals d? Yes, that will still be true. It can be put differently. We can, for example, subtract off the c. So ax plus by equals d minus c, which will appear a number. Or subtract off the d. Then it is like ax plus by plus c minus d equals 0. It works that way. One more tiny detail. The word normal means perpendicular. It is simply another word that means exactly the same thing. Mathematicians often use the word normal when referring to a vector that is perpendicular to a line. Then, that red vector is the normal vector to the line.

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