Explanation of the epipolar constraint in stereo imaging

Question

I am watching this video, in which the epipolar constraint is defined as

$x_l \cdot (x_l \times t)=0$

It means that the vector $x_l$ that passes through the observed point and the left camera origin is perpendicular to the normal of the epipolar plane, defined by that same vector, and the epipolar line.

What I fail to understand is, why is this a constraint at all?

Doesn't it hold for ANY two vectors $v$ and $w$ that $v \cdot (v \times w) = 0$?

Answer 1

Doesn't it hold for ANY two vectors v and w that v⋅(v×w)=0? -> Yes

but you should think about the later part of the lecture where this obvious equation is converted into an essential matrix equation.

By substituting one xl to xr you can convert the equation so that two cameras and a point are tied by this constraint.