Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Chapter 1, Problem 1.11P
Given the points M(0.1, -0.2, -0.1), N(-02, 0.1, 0.3), and P(0.4, 0, 0.1), find (a) the
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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
1.) Given the points M(0.1,−0.2,−0.1), N (−0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find:
a.) the dot product RM N · RM P
b.) the scalar projection of RM N on RM P
c.) the angle between RM N and RM P .
a.
Two vectors A and B are given at a point P(r, Ɵ, Φ) in space as
A = 10ar + 30aƟ – 10a Φ
B = 3ar + 10aƟ – 20a Φ
Determine:
2A – 5B
B
A X B
Repeat the above solution if the two vectors A and B given at a point P(r, Ɵ, Φ) in space reduced by 30 percent.
Discuss the differences in solution a and b above.
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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- Give the vector in cartesian coordinates that extends from B(4, 20degrees, 10degrees) to W(7, 120degrees, 85 degrees).arrow_forwardGiven 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_forwardGiven vector A = [5,–8,5] and C = [1,4,–3]. Which is the angle between these vector, if we take the dot product F = A•C? if not in the choices, choose the closestif not in the choices, choose the closestarrow_forward
- Given the points: M(0.1, -0.2, -0.1) N(-0.2, 0.1, 0.3) P(0.4, 0 , 0.1) Find the RMN + RMP Find the vector amparrow_forwarda. If the magnitudes of the two velocity vectors are V1 = 3 m/s and V2 = 2 m/s, determine their resultant.(b) If their resultant is a horizontal vector with magnitude of 4 m/s directed to the right, determine the magnitude of vectors V1 and V2.arrow_forwardGiven the points T (5, 20°, 120°) to P (2, 80°, 30°): find the unit vector in spherical coordinates at T that is directedtoward P.arrow_forward
- 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?arrow_forwardTwo points A(2,2,1) and B(3,-4,2) are given in the cartesian system. Obtain the vector from A to B and a unit vector directed from A to Barrow_forwardTwo points A(2,2,1) and B(3,-4,2) are given in the Cartesian system. Obtain the vectors from A to Band a unit vector directed from A to B.arrow_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_forward1.Give some practical examples of Scalar product and Vector product. 2. Bring out the importance of Curl of a vector with an application. 3. Give a reason why the dot product of two vectors is known as the Scalar product? 4.Give some practical applications of EM waves?arrow_forwardIf a scalar field φ(x,y,z)=3x2y-y3z2, calculate the gradient ∇φ at point M(1,-2,1).arrow_forward
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