4) Using tensor formalism, i.e. Kronecker delta, Levi-Civita symbol, and Einstein's summation convention, prove the following vector identities: (a) Ā × (B × T) = B (Ä · C) – T(A · B).

Q: Calculate Vf using suffix notation and the chain rule: ƒ(r) = 3(a ⋅r)² − a²r² (a is a vector…

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Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

Q: Consider the following. u = 9i + 4j, v = 8i + 2j (a) Find the projection of u onto v. (b) Find the…

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Q: Let I and g be unit vectors. Hence T-T= -G = 1. Calculate the inner products I (-1) and (T+g) -…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given that v=<x-y, z+y+9, z2> and the given curve is y=1-x2-z2,y≥0 To find: The value of ∬S…

Q: Show that (u - v) × (u + v) = 2(u × v)

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Q: (a) Given that V= əx ə a i+ j+ -k. Show that V.VB=V²B where is a scalar ду əz (b) If M and N are…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 8-b. Find the real part of the length of the vector v° = (5 + i, –2 + 2i, –1+i)

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A:

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

Q: grad (фu) —D и @ grad ф + ф grad u

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