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Problems 1.1 Given the two vectors A =2i +j and B =j + 2k, find the following: (a) A+B and IA+BI (b) 3A-2B (c) A. B (d) AxB and IAXBI

Problems 1.1 Given the two vectors A =2i +j and B =j + 2k, find the following: (a) A+B and IA+BI (b) 3A-2B (c) A. B (d) AxB and IAXBI

Power System Analysis and Design (MindTap Course List)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.55P
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Homework sheet 1 Chapter one Problems 1.1 Given the two vectors A =2i +j and B =j + 2k, find the following: (a) A+B and IA+BI (b) ЗА—2B (c) A. B (d) AxB and IAXBI 1.2 Given the three vectors A = i +j, B =2i + k, and C = 3j, find the following: (a) A.(B + C) and (A + B).C (b) A.(BxC) and (AxB).C (c) Ax(BxC) and (AxB)xC 1.3 Find the angle between the vectors A = bi + 2bj and B = bi + 2bj + 3bk. (Note: These two vectors define a face diagonal and a body diagonal of a rectangular block of sides b, 2b, and3b.) 1.4 Consider a cube whose edges are each of length 2. One corner coincides with the origin of an xyz Cartesian coordinate system. Three of the cube's edges extend from the origin along the positive direction of each coordinate axis. Find the vector that begins at the origin and extends (a) along a major diagonal of the cube; (b) along the diagonal of the lower face of the cube. (c) Calling these vectors A and B, find C = Ax B. (d) Find the angle between A and B. 1.5 Given the time-varying vector A = i at? +j 3bt? +k ct where a, b, andc are constants, find the first and second time derivatives dA/dt and dA? /dt?. 1.6 For what value (or values) of q is the vector A = iq + 5j + k perpendicular to the vector B = iq- qj + 4k? 1.7 Show that A.(B x C) is not equal to B.(A x C). 1.8 A small ball is fastened to a long rubber band and twirled around in such away that the ball moves in an elliptical path given by the equation r(t) = Ib cosút +j 3b sinýt where b and w are constants. Find the speed of the ball as a function of t. In particular, find v att =0 and at t= n/2w, at which times the ball is, respectively, at its minimum and maximum distances from the origin. 1.9 A buzzing fly moves in a helical path given by the equation r(t)=ib sinýt +jb cosýt + kct Show that the magnitude of the acceleration of the fly is constant, provided b, w, and c are constant.
Transcribed Image Text:Homework sheet 1 Chapter one Problems 1.1 Given the two vectors A =2i +j and B =j + 2k, find the following: (a) A+B and IA+BI (b) ЗА—2B (c) A. B (d) AxB and IAXBI 1.2 Given the three vectors A = i +j, B =2i + k, and C = 3j, find the following: (a) A.(B + C) and (A + B).C (b) A.(BxC) and (AxB).C (c) Ax(BxC) and (AxB)xC 1.3 Find the angle between the vectors A = bi + 2bj and B = bi + 2bj + 3bk. (Note: These two vectors define a face diagonal and a body diagonal of a rectangular block of sides b, 2b, and3b.) 1.4 Consider a cube whose edges are each of length 2. One corner coincides with the origin of an xyz Cartesian coordinate system. Three of the cube's edges extend from the origin along the positive direction of each coordinate axis. Find the vector that begins at the origin and extends (a) along a major diagonal of the cube; (b) along the diagonal of the lower face of the cube. (c) Calling these vectors A and B, find C = Ax B. (d) Find the angle between A and B. 1.5 Given the time-varying vector A = i at? +j 3bt? +k ct where a, b, andc are constants, find the first and second time derivatives dA/dt and dA? /dt?. 1.6 For what value (or values) of q is the vector A = iq + 5j + k perpendicular to the vector B = iq- qj + 4k? 1.7 Show that A.(B x C) is not equal to B.(A x C). 1.8 A small ball is fastened to a long rubber band and twirled around in such away that the ball moves in an elliptical path given by the equation r(t) = Ib cosút +j 3b sinýt where b and w are constants. Find the speed of the ball as a function of t. In particular, find v att =0 and at t= n/2w, at which times the ball is, respectively, at its minimum and maximum distances from the origin. 1.9 A buzzing fly moves in a helical path given by the equation r(t)=ib sinýt +jb cosýt + kct Show that the magnitude of the acceleration of the fly is constant, provided b, w, and c are constant.
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