MATH 253 Study Guide - Quiz Guide: Angle, Cross Product, Parallelogram
Document Summary
Solutions to homework assignment #1: sketch the curve r = 1 + cos (cid:18); 0 (cid:20) (cid:18) (cid:20) 2(cid:25); and (cid:12)nd the area it encloses. Figure 1: the curve r = 1 + cos(cid:18); 0 (cid:20) (cid:18) (cid:20) 2(cid:25) Are these vectors orthogonal? (c) ~a is a unit vector having the same direction as ~i +~j and ~b is a vector of magnitude. 2 in the direction of ~i + ~j ~k: Solution: (a) ~a (cid:1) ~b = 2 2 = 0: these vectors are orthogonal. (b) ~a (cid:1) ~b = (x2y3 x3y2)x1 + (x3y1 x1y3)x2 + (x1y2 x2y1)x3 = 0: these vectors are orthogonal. 2 (c) ~a = (~i + ~j) and ~b = 3 (~i + ~j ~k) and therefore ~a (cid:1) ~b = Solution: (a) let ~a = q p = ~j + ~k;~b = r p = ~i + ~k: then the area of the triangle is.
