Using practical examples of scalar fields f and vector fields E of your choice, describe with the aid of diagrams the physical meaning of the gradient ( Vf), divergence (VF) and curl (VxF). Gradient: Electromagnetic example + Non-electromagnetic example Divergence: Electromagnetic example + Non-electromagnetic example Curl: Electromagnetic example + Non-electromagnetic example

Q: (b) ||ū× w|| (u • w) (c) (d) (r+s) ux v + w s(v+w• w) × (rv)

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Q: Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

A: We have to find the scalar product a·b when (i). a=x+2y-z and b=2x+3y+z(ii). a=x-3y+z and b=2x+y+z

Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

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A: If the curl of a vector field F is zero then the vector field is conservative.

Q: ctor under linea

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A: Since     F→(x,y)=<-y, x2> The vector field of the function is

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Q: Linear Algebra: Explain the term "Vector basis" giving example to support your answer.

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A: Given that: Vector is in the direction of <5, -12> and length is 3.

Q: 6. Vector, scalar or meaningless? Explain. ») (ä - 5) + (7 - E) b) (å x 5) – (¿ x đ) c) dlã x )

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Q: Zero component of the curl For what vectors n is(curl F) ⋅ n = 0 when F = ⟨y, -2z, -x⟩?

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Q: Violet now comments that there are scalars a and B such that di DE = a EF × EG = B GF x GD State the…

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Q: example of a vector equation for a line in 3 dimensions which doesn’t intersect the plane at z = 0

A: Given that:a vector equation for a line in 3 dimensions which doesn’t intersect the plane at z = 0

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Q: (b) Sketch enough vectors in the vector field to get a sense of its geometric structure. (You should…

A: Given first order system:                                  dxdt= 1dydt = 0

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A: option a is correct

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A: The span of vectors are given as follows :

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A: The objective of the question is computing the values.

Q: Show how to use Hausman Test B₁ B₂ under Ho Consistent, Efficient Consistent, less Efficient under…

A: The Hausman test is  used to decide whether the estimate of an unknown parameter is consistent or…

Q: 1. (Vector Operations) Consider = and = k. (a) Find a unit vector in the opposite direction as a.…

A: Answer given below.

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