EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
7th Edition
ISBN: 8220100663659
Author: ULABY
Publisher: PEARSON
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Question 10
Consider the vectors A =4ax+2kaytaz and B = az+4ay-16a, what value of k the two vectors A and B will be orthogonal ?
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The following vectors are given: M=-10ax+4ay-8az and N=8ax+7ay-2az. Find the unit vector in the direction of -M+2N
Chapter 3 Solutions
EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
Ch. 3.1 - When are two vectors equal and when are they...Ch. 3.1 - Prob. 2CQCh. 3.1 - If AB = 0, what is AB?Ch. 3.1 - If AB = 0, what is AB?Ch. 3.1 - Is A(BC) a vector triple product?Ch. 3.1 - If AB = AC, does it follow that B = C?Ch. 3.1 - Find the distance vector between P1 = (1, 2, 3)...Ch. 3.1 - Find the angle AB between vectors A and B of...Ch. 3.1 - Prob. 3ECh. 3.1 - Vectors A and B lie in the y-z plane and both have...
Ch. 3.1 - If AB=AC, does it follow that B = C?Ch. 3.2 - A circular cylinder of radius r = 5 cm is...Ch. 3.3 - Why do we use more than one coordinate system?Ch. 3.3 - Prob. 8CQCh. 3.3 - Prob. 9CQCh. 3.3 - How is the position vector of a point in...Ch. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Find the directional derivative of V=rz2cos2 along...Ch. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.5 - Given A=e2y(xsin2x+ycos2x), find A.Ch. 3.5 - Given A=rrcos+rsin+z3z , find A at (2,0, 3).Ch. 3.5 - If E=RAR in spherical coordinates, calculate the...Ch. 3.5 - Verify the divergence theorem by calculating the...Ch. 3.5 - Prob. 17ECh. 3.6 - Find A at (2, 0, 3) in cylindrical coordinates for...Ch. 3.6 - Find A at (3, /6, 0) in spherical coordinates for...Ch. 3.7 - What do the magnitude and direction of the...Ch. 3.7 - Prob. 12CQCh. 3.7 - Prob. 13CQCh. 3.7 - Prob. 14CQCh. 3.7 - What is the meaning of the transformation provided...Ch. 3.7 - Prob. 16CQCh. 3.7 - Prob. 17CQCh. 3.7 - When is a vector field conservative?Ch. 3 - Prob. 1PCh. 3 - Given vectors A=x2y3+z, B=x2y+z3, and C=x4+y2+z2,...Ch. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Given vectors A=x+y2z3, B=x2y4, and C=y2z4, find...Ch. 3 - Given vectors A=x2y+z3 and B=x3z2, find a vector C...Ch. 3 - Given A=x(x+2y)y(y+3z)+z(3xy), determine a unit...Ch. 3 - By expansion in Cartesian coordinates, prove: (a)...Ch. 3 - Find an expression for the unit vector directed...Ch. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - A given line is described by x+2y=4. Vector A...Ch. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Given B=x(z3y)+y(2x3z)z(x+y), find a unit vector...Ch. 3 - Find a vector G whose magnitude is 4 and whose...Ch. 3 - A given line is described by the equation: y=x1....Ch. 3 - Vector field E is given by E=R5Rcos12Rsincos+3sin....Ch. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Use the appropriate expression for the...Ch. 3 - Prob. 26PCh. 3 - A section of a sphere is described by 0 R 2, 0 ...Ch. 3 - A vector field is given in cylindrical coordinates...Ch. 3 - At a given point in space, vectors A and B are...Ch. 3 - Given vectors...Ch. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Transform the vector A=Rsin2cos+cos2sin into...Ch. 3 - Transform the following vectors into cylindrical...Ch. 3 - Transform the following vectors into spherical...Ch. 3 - Find the gradient of the following scalar...Ch. 3 - For each of the following scalar fields, obtain an...Ch. 3 - The gradient of a scalar function T is given by...Ch. 3 - Prob. 39PCh. 3 - For the scalar function V = xy2 z2, determine its...Ch. 3 - Evaluate the line integral of E=xxyy along the...Ch. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Each of the following vector fields is displayed...Ch. 3 - Prob. 45PCh. 3 - For the vector field E=xxzyyz2zxy, verify the...Ch. 3 - For the vector field E=r10erz3z, verify the...Ch. 3 - A vector field D=rr3 exists in the region between...Ch. 3 - For the vector field D=R3R2, evaluate both sides...Ch. 3 - For the vector field E=xxyy(x2+2y2), calculate (a)...Ch. 3 - Repeat Problem 3.50 for the contour shown in Fig....Ch. 3 - Verify Stokess theorem for the vector field...Ch. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Verify Stokess theorem for the vector field B = (r...Ch. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Find the Laplacian of the following scalar...
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- Q1: Three vectors extending from the origin are given as r = 7ax + 3ay - 2a: r: =-2ax + 7ay – 3az r3 = 2ay + 3az Find the angle between ri - rz and ri-rsarrow_forwardAsap pleasearrow_forwardFind out the divergence of the following vector: A=4ax+3ay+2az ax, ay and az are unit vectors along x, y and z.arrow_forward
- The vector fields are defined as A= ap +2ao +3az, B = 0.4aap +0.4ßao -6az , both vectors are parallel then a and B are respectivelyarrow_forwardExample-4 Thank youarrow_forwardGiven two vectors R = 10 ax – 6ay + 5az and S = 0.1 ax + 0.2 ay + 0.3 az, calculate: a. Dot product of R and S b. Angle between R and S c. Cross product of the two vectors d. Unit vector from R to Sarrow_forward
- Ing to another question will save this response. Quèstion 1 Consider the vectors A =4a,+2ka,ta, and B=a,+4ay 16a, what value of k the two vectors A and B will be orthogonal ? 3.5 O 1.5 O 05 L A Moving to another question will save this response. P W SHIBA O O Oarrow_forwardGiven Å = & – ý + 22, B = -& + ŷ + 2 and Č = & + ŷ + 24. Vector (Å x . x B) x č is O x12 – ŷ12 x12 – ŷ12 + 2 -î12 + ŷ12 -x12 + ŷ12 + î O None of thesearrow_forward3- Find the distance between two vectors X -3 and Y = L-2]arrow_forward
- The vector projection of the vector A =ax -2ay + az on the vector B = 4ax - 4ay + %3D 7az is * O 0.94ax - 0.94ay + 1.64az -0.56ax + 0.84ay - 2.76az O -0.48ax + 1.76ay - 0.86az O -0.96ax + 1.58ay - 0.76az O Other:arrow_forwardQ1: Three vectors extending from the origin are given as ri = 7ax + 3ay – 2az r2 =-2ax + 7ay – 3az r3 = 2ay + 3az Find the angle between ri - r2 and ri - r3 %3Darrow_forwardIn dot product two vectors are perpendicular to each other, then the resultant vector is non zero. Select one: O True O Falsearrow_forward
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