MATH 241 Lecture Notes - Lecture 2: Cross Product, Dot Product, Paraboloid

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: Roohollah Ebrahimian

Document Summary

Recall from the previous lecture that we can find an equation of a line just by knowing a point on the line and a vector parallel to the line. We can do a similar thing with the equation of a plane. not need that the normal vector is on the plane. It just has to be perpendicular to it. Say we know a point p on the plane with coordinates (cid:1842)=(cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667). Next, say we want a vector perpendicular to the point. We call that a normal vector and denote it as =. We do take a random point on the plane and call it (cid:1842)(cid:2869) with coordinates (cid:1842)(cid:2869)=(cid:4666)(cid:1876)(cid:2869),(cid:1877)(cid:2869),(cid:1878)(cid:2869)(cid:4667). We let the position vectors and (cid:2869) be the position vectors for (cid:1842) and (cid:1842)(cid:2869) respectively. So the normal vector and the difference of the two position vectors will be perpendicular to one another since the position vectors are on the plane. That means their dot product will be zero.