Editing Geometric algebra (section)

=== Intersection of a line and a plane ===
[[File:LinePlaneIntersect.png|thumb|A line L defined by points T and P (which we seek) and a plane defined by a bivector B containing points P and Q.]]

We may define the line parametrically by {{tmath|1= p = t + \alpha \ v }}, where {{tmath|1= p }} and {{tmath|1= t }} are position vectors for points P and T and {{tmath|1= v }} is the direction vector for the line.

Then
: <math>B \wedge (p-q) = 0</math> and <math>B \wedge (t + \alpha v - q) = 0</math>
so
: <math>\alpha = \frac{B \wedge(q-t)}{B \wedge v} </math>
and
: <math>p = t + \left(\frac{B \wedge (q-t)}{B \wedge v}\right) v. </math>