From 1.31 1.32 and 1.33 show all work 1.31 4 Number of independent scalar equations from one vector equation. (Section 2.9.5)Consider the vector equation shown to the right that can be usefulfor static analyses of any system S.System typeInteger(s)Complete the blanks in the table to the right with all integers thatcould be equal to the number of independent scalar equationsproduced by the previous vector equation for any system S.1D (line)2D (planar)Hint: See Homework 1.30 for ideas.3D (spatial)Note: Regard 1D/linear as meaning F can be expressed in terms of a single unit vector iwhereas 2D/planar means F can be expressed in terms of two non-parallel unit vectors î and j,and 3D/spatial means F can be expressed in terms of three non-coplanar unit vectors î, j, k.1.32 4 Vector concepts: Solving a vector equation (just circle true or false and fill-in the blank).Consider the following vector equation written in terms of the scalars r, y, zand three unique non-orthogonal coplanar unit vectors â1, â2, â3.(2x – 4) â1 + (3 y – 9) âz + (4z – 16) âz = ōThe unique solution to this vector equation is r = 2, y = 3, z = 4. True/False.Explain: âz can be expressed in terms of ấ¡ and âg (i.e., âz is a linear combination of â1 and âs).Hence the vector equation produceslinearly independent scalar equations.1.33 A vector revolution in geometry. (Chapter 2)The relatively new invention of vectors (Gibbs z 1900 AD) has revolutionized Euclidean geometry(Euclid z 300 BC). For each geometrical quantity below, circle the vector operation(s) (either thedot-product, cross-product, or both) that is most useful for their calculation.Length:Angle:Area:Volume:1.34 † Microphone cable lengths (non-orthogonal walls) "It's just geometry". Show work.A microphone Q is attached to three pegs A, B, C by three cables. Knowing the peg locations,microphone location, and the angle 0 between the vertical walls, express LA, LB, LC solely in termsof numbers and 0. Next, complete the table by calculating LB when 0 = 120°.Hint: To do this efficiently, use only unit vectors û, v, w, and do not introduce an orthogonal set of unit vectors.Hint: Use the distributive property of the vector dot-product as shown in Section 2.9.1 and Homework 2.4.Note: Synthesis problems are difficult. Engineers solve problems. Think, talk, draw, sleep, walk, get help, .Distance between A and B20 m15----------Distance between B and CDistance between N, and B15 m8 m7 mDistance along back wall (see picture)Q's height above N.Distance along side wall (see picture)5 m8 mLA: Length of cable joining A and QLB: Length of cable joining B and QLe: Length of cable joining C and Q16.9 m8.1 m14.2 m1.Note: The floor is horizontal, the walls are vertical.Q/ No = 7û + 5ý + 8 wResult:LA =202 168 cos(0)LB =Lc = V137 -cos(0)62Homework 1: Vectors - basis independentCopyright © 1992-2017 Paul Mitiguy. All rights reserved.目回回

1.31 Given: The vector equation is, F⇀S=0 System type is given as 1D, 2D and 3D. Explanation: For…

1.31 & Number of independent scalar equations from one vector equation. (Section 2.9.5) Consider the vector equation shown to the right that can be useful for static analyses of any system S. System type 1D (line) Integer(s) Complete the blanks in the table to the right with all integers that could be equal to the number of independent scalar equations produced by the previous vector equation for any system S. 2D (planar) Hint: See Homework 1.30 for ideas. 3D (spatial) Note: Regard ID/linear as meaning F whereas 2D/planar means F can be expressed in terms of two non-parallel unit vectors i and j, and 3D/spatial means F can be expressed in terms of three non-coplanar unit vectors i, j, k. can be expressed in terms of a single unit vector i

1.31 & Number of independent scalar equations from one vector equation. (Section 2.9.5) Consider the vector equation shown to the right that can be useful for static analyses of any system S. System type 1D (line) Integer(s) Complete the blanks in the table to the right with all integers that could be equal to the number of independent scalar equations produced by the previous vector equation for any system S. 2D (planar) Hint: See Homework 1.30 for ideas. 3D (spatial) Note: Regard ID/linear as meaning F whereas 2D/planar means F can be expressed in terms of two non-parallel unit vectors i and j, and 3D/spatial means F can be expressed in terms of three non-coplanar unit vectors i, j, k. can be expressed in terms of a single unit vector i

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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