Finding the Normal Vector and Equation of a Line Perpendicular to 2x + y = 4

[imb3cile]

the equation of a straight line is given by 2x + y = 4

(a) find the vector equation of a unit normal from the origin to the line and (b) the equation of a line passing through P(0,2) and normal to 2x + y = 4.


i know i need to use the dot product some how but i am utterly confused as to where to begin! please help.

i think first the vector equation for the given line is r = < 1 , -2 > then i need to dot r with r_perp and set equal to 0? i am very confused. thanks!

 

[I like Serena]

Welcome to PF, imb3cile!

The general equation of a line is (\vec n, \vec x) = d
In this equation \vec n is a normal vector to the line, \vec x is the vector with your coordinates x and y, and d is an arbitrary constant, that creates an offset to the origin.
The parenthesis around the 2 vectors indicate that the dot product is taken.

If the vector n would have components a and b, this would turn out as: ax + by = d

Can you see from your own equation what the normal vector n would be?

For part (a) you would need a multiple of this vector, such that if you fill it in for x and y, it matches the equation.