Equations of Lines and Normal Vectors

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:ArialMT;color:#000000;} .ft02{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Equations of lines and normal vectors We use numbers now, but you can substitute any letter for each variable. If you have axplus 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 tothe 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 dminus c, which will appear a number. Or subtract off the d. Then it is like ax plus by plus cminus d equals 0. It works that way. One more tiny detail. The word normal means perpendicular. It is simply another word thatmeans exactly the same thing. Mathematicians often use the word normal when referringto a vector that is perpendicular to a line. Then, that red vector is the normal vector to the line.