Mathematics 1229A/B Lecture Notes - Lecture 7: Cross Product, Parametric Equation

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Olds

Document Summary

Recall: a point parallel equation is given as (t) = (cid:2198) + t . Replacing (cid:1873) as (cid:1869) - (cid:1868) we get: (t) = (cid:2198) +t ((cid:2199) (cid:2198) ) (t) = (1 t) (cid:2198) + t(cid:2199) . After expanding the equation and placing coefficients together we get the two-point form equation: Math1229a -lecture #7- lines and planes: two point form equations for a line. Let us consider a line a through two points, p and q. The direction vector for line a will be in the form: Example 1: write a two-point form equation for the line p (1,2,3) and q (-1,1,2). Example 2: write a two-point form equation of the line through p (1,0) which is perpendicular to the vector (2,3). If (2,3) is perpendicular to the line then you switch the numbers and add a negative sign to either number to get the orthogonal. This means that (cid:1873) = (3, -2) is a direction vector for the line.