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I want to confirm this:

a=8, b=5, c=7

Count out the distance from origo to planet z = ax + by + c in three different ways.

1) With the aid of linear algebra and geometry (no derivates!).

Normalvector is: (a,b,-1) , the length * (8,5,1) = p ,(p=point)

p=(x,y,z) gives 8s=x , 5s=y. -s = 8x+5y+7 => -90s=7 => s=-7/90 => x = -56/90 , y = -35/90 , z = 7/90 , Is this correct?

2) Through solving one optimization problem in two variables without bee conditions.

q^2 = (ax+by+c)^2 where q is the distance

uses the df/dx = df/dy = 0 and gets:

130x+80y+112=0

80x+52y+70=0

and then solves what x,y,z is ? Or have i done something wrong?

3) Through using Lagranges multiplier method

I havent done this because i dont know how to use this method, can anyone help me with this?

I want some help to confirm if i am solving this correctly.