MATH115 Study Guide - Quiz Guide: Linear Combination, Dot Product

• School: University of Waterloo
• Department: Mathematics
• Course: MATH115
• Professor: Martin Pei

Document Summary

Math 115 fall 2012 lab 1 solutions: {12 marks} consider the two vectors (cid:126)u = The dot product (cid:126)u (cid:126)v = 2 ( 1) + ( 5) 4 + ( 1) 0 = 22. Since this is not 0, (cid:126)u and (cid:126)v are not orthogonal. (b) determine ||2(cid:126)u + (cid:126)v||. , so ||2(cid:126)u + (cid:126)v|| =(cid:112)32 + ( 6)2 + ( 2)2 = 7. 3 6 2 (c) determine a scalar equation of the plane containing the point (7, 3, 4) whose normal vector is (cid:126)u. So an equation for the plane is 2x1 5x2 x3 = 3. (d) write (cid:126)v as the sum of two nonzero orthogonal vectors, one of which is a scalar multiple of (cid:126)u. We are looking for the projection of (cid:126)v onto (cid:126)u, and its perpendicular part. proj(cid:126)u ((cid:126)v) = perp(cid:126)u ((cid:126)u) = (cid:126)v proj(cid:126)u ((cid:126)v) = One point on the line is p , so one possible.