Example 20.35. Evaluate z-3 dz, where C is the circle 2 + 2z + 5 (i) |2+ 1- i| = 2,
Q: A charged particle moves with a uniform velocity 4.3 ŷ (m/s) in a region where E = 192 (V/m) and B =…
A: Given: Charged particle moving velocity, v→=4.3y^ ms Electric field, E→=19z^ Vm Magnetic field…
Q: Q2 (i) Evaluate ,7 dz, where C is the positively oriented circle lz - 1| 1.
A: Here we have to integrate the complex integral I=∮(z¯)2 dzalong a circle z-1=1, x-12+y2=1 ;this…
Q: 4. If f is a scalar field and F, G are vector fields, prove that: V. (F x G) = G (V × F) – F (V x G)
A: f is a scalar field and F, G are vector fields
Q: 69. For the following vectors Ả = 5ì – 7ỷ + 2: B = oi + 33 + 112 -9î + 43 – 9£ Ď = li+0j – 3
A: (a) A→×B→.D→ The cross product of two vectors A and B is i^ j^ k^ 5…
Q: What are the indices (Miller indices) of a plane whose intercepts with three axes are 2,4,2,…
A: take the reciprocal of the intercepts. We then obtain 12,14,12
Q: If two vectors ? = 4? + 6? − 8? and ? = 6? − 8? + 4? are added together describe the characteristics…
A: “Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: Convert these complex numbers to polar form and check yo such as Mathematica. (If using Mathematica,…
A: A complex number can be converted from rectangular to polar form and vice versa as:
Q: Express the vector field W=(x^2-y^2)i +xzk in spherical coordinates at P(4,30degrees,120degrees).
A:
Q: Evaluate the double integral 3 + 2х + Зу dх dy : y=0 Jx=0 Select one: O 22/3 о 13/3 O 35/2 O 12
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Q: 4) Solve F.dr using Stokes' theorem for yzi✦ zi‡ yk„where S is the cylinder x² + y² = 4 between -3 ≤…
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Q: Consider R =À +B+D which of the following is incorrect? O All choices are incorrect O Ř =JTRj? +…
A: The resultant vector is shown as .
Q: 8. [-/2 Points] DETAILS SERCP11 2.XP.011. MY NOTES ASK YOUR TEACHE A certain cable car in San…
A: The instant when dog jumps on the track, the equation which defines that is, d=ut+12at2 7.40 sec…
Q: Sketch the curve with the given polar equation. r= 4 + sin 8 y y
A: Solution: Given data, r = 4 + sin θ
Q: Physics problem 23.36 (please assume the dot given is the origin, and that the X-axis is horizontal…
A: The figure can be drawn as follows: Let the charges be named A, B and C and their electric field be…
Q: Calculate the areas of the following surfaces using the differential surface area dS p=2,0 ≤z≤ 5,…
A:
Q: 3 - Given a scalar field T = (x+3)y² sin(2z) and a vector field A= r*yi+ y?(z+5)k, calculate (3) %3D…
A: The given scalar and vector fields are T=x+3y2sin2zA=x3yi+y2z+5k
Q: Given the following matrix 3 3 1 5 Find its two eigenvectors. (A 3 and H2 0. B 3 and A, !! R -3 and…
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Q: -29 +9 (2) What is E in magnitude and direction at the center of the square shown in the figure?…
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Q: For any two vectors A and B, if A.B =0 then the angle between them is Zero aO degree 90.b O degree…
A: Given here for two vectors A and B if A→. B→ =0we are asked what is the angle between vector A and…
Q: 4. Vectors A,B and C form a triangle, as shown in the figure. Prove the law of cosines, |C|? = |A]?…
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Q: Draw the vector V3, where V3=V1+V2, and calculate the value of V3
A: phase difference between V1 and V2 ϕ ≃ 5 × π 6 - ( - π 3 ) - 2.047 ≃ 7 × π 6 -…
Q: two complex numbers z1 = 7.9 + i 21.1 and 22 = 14.4 - i 32.2 Find the the magnitude of the z where…
A: Given : z1=7.9+21.1iz2=14.4-32.2i
Q: Consider the following LP. (Primal problem) Min z = 24x1 -12x2 + 4x3 %3D s.t. 3x1 - 3x2 2 3 4x1 +…
A: Given : Min z = 24x1 - 12x2+4x3 3x1 -3x2 ≥ 34x1+2x2…
Q: An electron travels with = 4.00 x 106 m/s through a point in space where E=(2.10 x 105 - 2.10 x 105)…
A: Given: Velocity Electric field Magnetic field Charge on electron Required: Force on the elctron .
Q: Given: a = 2.51 m, |Q| = 67 µC My Question: How can I find E1 (if the x-axis is located at +9a) and…
A: Given that: a=2.51 mQ=67μC=67×10-6 C
Q: Find the singular point of the rational function f(z)=z/(z+i) * O z=-i O z=1 O z=i O z=-1 Find f'(z)…
A: i. Fz=zz+i*=zz*-isingular point , z*-i=0z*=iz=-i
Q: 16. A vector whose divergence is zero everywhere is said to be solenoidal and a vector wh curl is…
A: 16)a ϕ and ψ are differentiable functions, such that A→=∇→ϕand B→=∇→ψR.T.P: A→×B→ is…
Q: Given a vector field A = 5x ^ 2(sin (pi*x)/2) i, find V.A at x = 1
A: Vector A = 5x².(sin (pi.x)/2)i
Q: Problem 1. Find a b if lal = 10, b| = 9, and the angle between a and b is - radians. ab=
A: Given, a=10 b=9 angle θ=-π6rad = -30 degrees a . b = ? The…
Q: E = ? at (a) x 2h
A:
Q: 7. a) Find the divergence of the vector field G(x, y, z)= exi+ln(xy) j+exyz k at (0.2, -31 b) Find…
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Q: z-3 Evaluate $c 2?+2z+5 1 and C : |z+1 – i| = 2. dz = "(i – 2). dz where C : Ans. fo z dz = 0 and fo…
A: Given, ∮ C z-3z2+2z+5dz
Q: (a) E = k (xyî + 2yzj + 3xzk) (b) E = k (y²î + (2yz + z²) ĵ + 2yzk) (c) E = k (yzi+xzĵ+ xy. xyk)
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Q: V = {0, (0 < x < a, 0 s y Sa) {00, other values of x and y Answer for the particle with mass m under…
A: Since you have asked multiple question, we will solve the first question for you. If you want any…
Q: 40 三 In the figure, if A = 15, and B= 10. What is the magnitude of AxB? 41
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Q: честоп 1 > frond. (y+z)i + (x+₂)j + (x+y) û -Ġ= 1²¹² i + y² G 1`72 - M = j yz ² lyzi + 2xz j + 3xy 2…
A: We have given some vectors then we have to find the divergence of these vectors. The required…
Q: If r is going from the origin to the point (x,y,z) and r#0 I prove the following relations: V«($) -…
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