MATH 2001 Study Guide - Midterm Guide: Vector Projection, Paraboloid, If And Only If
24 Oct 2015
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2 vectors and the geometry of space (stewart"s chapter 12) 2. 1 vectors: unit vector in the direction of (cid:126)v is (cid:126)u = (cid:126)v|(cid:126)v, orthogonal means perpendicular. The orthogonal projection of u onto v is denoted projvu and the scalar component of u in the direction of v is denoted scalvu. projvu = |u| cos (cid:18) v (cid:19) |v| = (cid:17) (cid:16) u v v v v scalvu = |u| cos = u v. U2v3 u3v2 u3v1 u1v3 u1v2 u2v1. Note: u v is orthogonal to both u and v and the direction is de ned by the right-hand rule. 2. 1. 3 triple product: the volume of the parallelepiped determined by (cid:126)a, (cid:126)b, and (cid:126)c is v = (cid:126)a ((cid:126)b (cid:126)c) = ((cid:126)a (cid:126)b) (cid:126)c. 2. 2 lines: parallel lines have proportional direction vectors, skew lines neither intersect nor are parallel. Check for intersection by setting the parametric equations equal and solving the system.
