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Let E:=Exi^+Eyj^+Ezk^ and H:=Hxi^+Hyj^+Hzk^ be two vectors assumed to have continuous partial derivatives (of second order at least) with respect to position and time. Suppose further that E and H satisfy the equations:∇⋅E=0,∇⋅H=0,∇×E=−1c∂H∂t,∇×H=1c∂E∂tprove that E and H satisfy the equation∇2Ei=1c2∂2Ei∂t2 and ∇2Hi=1c2∂2Hi∂t2Here, i=x,y or z.

Let r=xi^+yj^+zk^ and r=r .Show that:∇(lnr)=rr2. and∇×(rnr)=0.

 Find the angles between the force F = 1200𝐢 + 800𝐣 − 1500𝐤 N and the x-, y-, and z-axes. Show your results on a sketch of the coordinate system.

A= x2zi + xy j +y2z k, B = yz2 +xz j + x2z k, find grad(A.B)

prove : div cur l f =0

An oil of is flowing through a Venturimeter having inlet diameter 20 cm and throat diameter 10 cm. The oil-mercury differential manometer shows a reading of 25 cm. Calculate the discharge of oil through the horizontal Venturimeter. Take Cd = 0.98.

For the velocity potential function, φ = x^2 - y^2 . Find the velocity components at the point (4, 5).
If for a two dimensional potential flow, the velocity potential is given by : φ = 4x(3y - 4), determine the velocity at the point (2, 3). Determine also the value of stream function ψ at the point (2, 3).
If F=A×(B×C) where A=5it^2 + (3t-2)j + 6tk; B=2i+4tj+3(1-t)k and C=4ti+5jt^2 -3tk evaluate integral of Fdt with limits zero to one.
What do you understand by unit tangent vector
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