Chapter 1 Topics in Analytic Geometry

•MA112 Section 750001: Prepared by Dr.Archara Pacheenburawana 40F 2F 1 +F 2F 1Physicists and engineers call F 1 +F 2 the resultant of F 1 and F 2 , and they say that theforces F 1 and F 2 are concurrent to indicate that they are applied at the same point.Example 3.12 Suppose that two forces are applied to an eye bracket, as show in Figurebelow. Find the magnitude of the resultant and the angle θ that it makes with the positivex-axis.y‖F 2 ‖ = 300N40 ◦ ‖F 1 ‖ = 200N30 ◦xSolution .........3.3 Dot Product; ProjectionDefinition of the Dot ProductDefinition 3.3 If u = 〈u 1 ,u 2 〉 and v = 〈v 1 ,v 2 〉 are vectors in 2-space, then the dotproduct of u and v is written as u·v and is defined asu·v = u 1 v 1 +u 2 v 2Similarly, if u = 〈u 1 ,u 2 ,u 3 〉 and v = 〈v 1 ,v 2 ,v 3 〉 are vectors in 3-space, then their dotproduct is defined asu·v = u 1 v 1 +u 2 v 2 +u 3 v 3Note that the dot product of two vectors is a scalar. For example,〈4,−3〉·〈3,2〉 = (4)(3)+(−3)(2) = 6〈1,2,−3〉·〈4,−1,2〉 = (1)(4)+(2)(−1)+(−3)(2) = −4