Introduction
日本語 ver
Plane in two dimention is expressed following.
\{x|<x,v> = 0\}
however, v is orthogonal vector for plane and not zero vector.
Proof
\forall k \in \{x|<x,v> = 0\},k is fulfill this form.
<k,v> = 0
Now, because k and v in two dimentinal space, each vector express following.
k = (k_1,k_2)
v = (v_1,v_2)
Thus, <k,v>=k_1v_1 + k_2v_2=0
Change this equation.
k_2 = -\frac{v_1}{v_2} k_1
This equation is plane that slope is -\frac{v_1}{v_2}.
Q.E.D
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