Question

Find the normal form of the equation of the line in R2 that passes through P = (2,-1) and is perpendicular to the line with general equation 2x - 3y = 1. I know that vector n = [2,3] and I know I have to do the dot product with (x,y) and point p. n(dot)x = n(dot)p In the question it says that P is (2,-1) but when I work it out shouldn't I get the right half equal to 1? Please help.

Answer 1

is this normal form http://www.solitaryroad.com/c426.html

Answer 2

x cos α + y sin α - p = 0

Answer 3

no it isn't sorry.

Answer 4

the line 2x - 3y = 1 has direction vector [ 2 3 ]

Answer 5

I take that back, solve for y

Answer 6

hello

Answer 7

hi

Answer 8

(2,-3) are coordinates of the normal vector

Answer 9

okay

Answer 10

another trick is, the direction vector of a line will always be t*(1, m) where m is the slope

Answer 11

the slope of this line is 2/3, so t * ( 1 , 2/3) , and scale it by 3 , so the direction vector is
(3,2)

Answer 12

thats cool!