show that velocity and acceleration are contravariant vectors and that the gradient of a scalar field is a covariant vector.

Q: A=(2x2-3y)ax+(2x-y2)ay   Prove the Stokes theorem for the triangular linear path in the shape that…

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Q: A charged particle is on an x-y plane. The particle starts from the origin, and begins by moving…

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Q: Explain the significant of the Curl of a vector and discuss what exactly is the essence of the del…

A: Have a look?

Q: Fompute the curl of the vector field F(r, o,0) = res+ cot o eg

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Q: The uniform vector field A = ay can also be expressed as?

A: If it is an MCQ, options would have aided in providing accurate answer.

Q: Q3- (a) Show that for what values of X,Y and Z the transformation of A = is orthogonal and then show…

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Q: In a vector field V = (x^a, y^b, z^c) what is the value of ∇.V at (x, y, z) = (d, e, f) with a = 3,…

A: The divergence is given by,  div=ddxx^+ddyy^+ddzz^Given vector field V is, V=xx^+yy^+zz^

Q: What is the angle between vectors A - 2i + 3j + k and B- 3i • 2j + K? O 21.79 O 42.88° 85.90° O…

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Q: H=ре салфар te'sing an tpar At point (1,5,6) find: a) H⋅ax b) H x do c) The vector component of H…

A: Given, H=ρzcosφaρ+e-2sinφ2aφ+ρ2az

Q: Find the divergence of the vector field. (V.V=V + OV₂ + 2/₂V₂) дх дz V(x, y, z) = (x²y, 3y, 5) =…

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Q: Q2 Compute the curl of the vector field F(r,o,0) =res+ cot o ee in spherical coordinates.

A: In spherical coordinate system, three basic parameters are the polar coordinate r, the azimuthal…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force triangles, to…

A: The orientation of the for 240 N from the positive x-axis is, The orientation of the for 180 N from…

Q: x²y°z* , e" sin(y) In(z). 2.3.4 g(x, y, z) = h(x, y, z)

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Q: A particle moves in the xy-plane under influence of the force field F = -kx-ky 1. Prove that the…

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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: Assume = 36 and H = 4. Determine the x-component of H.

A: Given: The angle is alpha = 36 degree The magnitude of the vector H = 4 units

Q: PE = kx'/2 PE, Egla c. d. =hc/. Туре? Туре? a = F/m f. KE = (1/2)mv? KE e. a F m Type? Type?

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Q: directed

A: The forces can be represented as,

Q: A,B and C are three non-collinear, non-coplanar vectors. What can you say about direction of…

A: Let the cross product of

Q: A charged particle is on an x-y plane. The particle starts from the origin, and begins by moving…

A: The problem is about a sum of two vector displacements in x-y plane. We resolve the vectors into…

Q: Find the magnitude of the vector {-2,0}.

A:

Q: Express the vector field W=(x^2-y^2)i +xzk in cylindrical coordinates at P(6,60degrees,-4).

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Q: Show that the directions of the isoline and the gradient line at any given points in a scalar field…

A: Prove that the gradient line and the isoline are orthogonal to one another at all points in a scalar…

Q: Let 3i−j+ 4k, 7j−2k, i−3j+k be three vectors with tails at the origin. Then theirheads determine…

A: Given that  Vector  OA→ = 3i^-j^+4k^OB →=7j^ - 2k^OC→ = i^-3j^+k^

Q: A vector field V is irrotational if ∇ × V = 0. Find constants a, b, c   so that V =(−4x−3y+az)i +…

A: Given value--- V =(−4x−3y+az)i + (bx+3y+5z)j + (4x+cy+3z)k . ∇ × V = 0. We have to find--- value…

Q: Determine the x. M. and z scalar components of the force. F= 900 N 60° 35

A: The values of components are given by: