MATH 210 Study Guide - Final Guide: Vector Projection, Unit Vector, Cross Product

• School: UIC
• Department: Mathematics
• Course: MATH 210
• Professor: All

Document Summary

Problem 1 solution: complete each of the following: (a) find a set of parametric equations for the line through (1, 1, 2) and (0, 2, 3). (b) consider the vectors v = h 1, 1, 2i and w = h2, 2, 4i. Solution: (a) in order to nd a set of parametric equations for the line, we need a point p0 on the line and a vector v parallel to it. A vector parallel to the line is the vector from the. V = h1 0, 1 ( 2), 2 ( 3)i = h1, 1, 5i. The vectors are not perpendicular because the dot product: V w = ( 1)(2) + (1)( 2) + (2)(4) = 4 is nonzero. Therefore, the vectors are neither parallel nor perpendicular. Problem 2 solution: find the equation for the plane containing the point (1, 2, 3) and the line whose vector equation is r (t) = h1 t, t, 2 + 4ti.