MATH214 Final: Math 214 complete comprehensive study guide

• School: University of Alberta
• Department: Mathematics
• Course: MATH214
• Professor: Rene Poliquin

Document Summary

The main topics are: vectors, unit vectors, equations of lines and planes, dot product, projections, cross product, distance to a plane, quadratic sur- faces. You use the dot product to determine if two vectors are orthogonal (per- pendicular) whereas you use the cross product to determine if two vectors are parallel. You use the cross product when you need to produce a vector that is orthogonal to two other vectors (as in nding the equation of a plane). To write the equation of a plane you need to produce a vector that is normal (orthogonal) to the plane. A vector is a doohickey (fancy math term) with direction and magnitude. Notation: < a, b, c > is a vector whereas (a, b, c) is a point in r3. The magnitude of ~u =< a, b, c > in r3 is |~u| = a2 + b2 + c2 so that.