Basic Intersections

Abstract

When line equations are given: Consider two lines

$$ \gamma _0 = \overline {(a_0 ,b_0 ,c_0 )^T } $$

and

$$ \gamma _1 = \overline {(a_1 ,b_1 ,c_1 )^T } $$

. In the ωXY vector space, these lines represent two planes that pass the origin and are normal to vectors γ₀ and γ₁ respectively. If the line

$$ \gamma = \overline {(a,b,c)^T } $$

goes through the intersection of these two lines, then vector γ lies on the plane formed by γ₀ and γ₁ That is, γ, γ₀ and γ₁ are linearly dependent.