MATH 210 Study Guide - Final Guide: Curve, Scilab, Cross Product
Document Summary
Problem 1 solution: consider three position vectors (tails are the origin): Solution: (a) since the tails of the given vectors are at the origin, the tips of the vectors are the points. U = (1, 0, 0), v = (4, 0, 2), and w = (0, 1, 1), respectively. The plane containing the tips has n = Using u = (1, 0, 0) as a point on the plane, an equation for the plane is. 2(x 1) 5(y 0) + 3(z 0) = 0 (b) the line perpendicular to the plane in part (a) is parallel to the plane"s normal vector. Thus, since h 2, 5, 3i is parallel to the line and the origin (0, 0, 0) is on the line, the vector equation for the line is. R (t) = h0, 0, 0i + t h 2, 5, 3i. Solution: (a) by de nition, the curvature of a curve parametrized by r (t) is given by the formula.
