Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 1, Problem 1.15P
Three
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1. Determine the initial point of the vector <2, 4, -1> whose terminal point is (3, -2, 2)
2. Find the magnitude and angle of the resultant vector if the given vectors are V1=-7i+7J and V2=6i-9j
3. for what values of "a" and "b" are the vectors <a-b, 2> and <4, a+b> equal?
Given points P (2,5, -1), Q (-1, -4,1), T (5,0,2), find the unit vectorsa. the unit vectors RPQ, RQT, and RTPb. the length of the perimeter of the triangle PQTc. the vector projection of RPQ on RPT
Two vector fields are F=-10ax + 20x(y-1)ay and G= 2x^2yax - 4ay + zaz. For the point P (2, 3, -4), find:
a. |F|: F at (2, 3, -4)
b. |G|: G at (2, 3, -4)
c. The unit vector in the direction of F-G
d. The unit vector in the direction of F+G
Chapter 1 Solutions
Engineering Electromagnetics
Ch. 1 - If A represents a vector two units in length...Ch. 1 - Vector A extends from the origin to (1, 2, 3), and...Ch. 1 - 1.3 The vector from the origin to point A is given...Ch. 1 - A circle, centered at the origin with a radius of...Ch. 1 - An equilateral triangle lies in the xy plane with...Ch. 1 - Find the acute angle between the two vector...Ch. 1 - Given the field F=xax+yay. If F. G =2xy and FĂ— G...Ch. 1 - Prob. 1.8PCh. 1 - A field is given as G=[25/(x2+y2)](xax+yay). Find...Ch. 1 - Prob. 1.10P
Ch. 1 - Given the points M(0.1, -0.2, -0.1), N(-02, 0.1,...Ch. 1 - 1.21 Write an expression recrangu1ar components...Ch. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Three vectors extending from the origin are given...Ch. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Exercise in cylinder components ;(a) the vector...Ch. 1 - Prob. 1.22PCh. 1 - The surfaces p=3,p=5,=130o,z=3andz=4.5 define a...Ch. 1 - Two unit vectors, a1 and a2, lie in the xy plane...Ch. 1 - Prob. 1.25PCh. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - A vector field is expressed as F = Az az where A...Ch. 1 - Consider a problem analogous to the varying wind...
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- Given three points: M(-1, 2, 1), N(3, -3, 0) and P(-2, -3, -4), find the ff: a. RMN b. RMN +RMP c. |rm| d. Unit Vector amparrow_forwardIf a scalar field φ(x,y,z)=3x2y-y3z2, calculate the gradient ∇φ at point M(1,-2,1).arrow_forwardPlease answer and write correctly and neatly. Given the vector field Ā= 2x2y ax – 2(z-x) ay + 3xyz az:a. Find Ā at P(2,-3,4)b. A unit vector in the direction of Ā at P.c. The scalar equation of the surface on which |A|=100d. The y-coordinate of Q (-3,y,5) if |AQ|=100 and y>0e. The distance between P and Qarrow_forward
- A vector field S is expressed in rectangular coordinates as S = {125/ [(x − 1)2+(y – 2)2 +(z + 1)}}{(x — 1)ax +(y — 2)ay +(2+1)a;}. (a) Evaluate S at P(2, 4, 3). (b) Determine a unit vector that gives the direction of S at P. (c) Specify the surface f(x, y, z) on which |S| = 1.arrow_forwardGive the vector in cartesian coordinates that extends from B(4, 20degrees, 10degrees) to W(7, 120degrees, 85 degrees).arrow_forwardQ2: A force F with a magnitude of 100 N is applied at the origin O of the axes x-y-z as shown. The line of action of F passes through a point A whose coordinates are 3 m, 4 m, and 5 m. Determine (a) the x, y, and z scalar components of F, (b) the projection Fxy of F on the x-y plane, and (c) the projection FOB of F along the line OB.arrow_forward
- Given points A(8, -5, 4) and B(-2, 3, 2), find: (a) the distance from A to B; (b) a unit vector directed from A towards B; (c) a unit vector directed from the origin toward the midpoint of the line AB; (d) the coordinates of the point on the line connecting A to B at which the line intersects the plane z = 3.arrow_forwardA charge QA = 20μC is located at A(−3, 2, 4), QB = 30μC is located at B(2, 1, 4), and a charge QC = 50μC is at C(5, 8,−2) in free space. If distances are given in meters, find: (a) vector AB; (b) vector AC. Determine the total vector force exerted on QA by QB and QC. (Draw the diagram)arrow_forwardUsing the coordinate system named, give the vector at point A (5, -4, 6) that extends to B (-1, 5, 3) a. Cartesian b. Cylindrical c. Sphericalarrow_forward
- If a scalar field Ø = 3(x2y − y2x) Calculate the gradient at Point(1, -2, -1)arrow_forwardThe ff vector fields are given: A = -10ax + 20x(y-1) ay B = 2x²y ax - 4ay + zaz For the given point P (2, -3, 4) find: a. Magnitude of Vector A b. Magnitude of Vector B c. Unit vector in the direction of (A+B) d. Unit vector from B to Aarrow_forwardFind the divergence of the vector: D = ρ2cosΦaρ at (1, 300, -5)arrow_forward
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