subject
Mathematics, 11.02.2021 22:10 MichealM7668

In lecture we introduced the Kronecker delta dij and the Levi-Civita symbol Eik which let us express the dot product and cross product of vectors in our usual three-dimensional space in terms of components. You should use Einstein summation convention (any re- peated index is summed over) throughout this problem. 1.01 Derive the vector triple product identity Āx (B x T) = (Ā. C)B – (A: BC us- ing the Kronecker delta and Levi-Cevita symbol. Note we have used the 'dot notation, e. g. (Ā• C) = (A, C). Carefully explain and/or justify each step you take (e. g. "by the an- tisymmetry of Eijk...")! Hint: Start with the left-hand side. Since both sides are vectors, we really want to show the component-version of the identity, (A ~ (B x ©))' = (A.Č)Bİ – (Ā• B)C'. 1.02 Using index notation, show Lagrange's identity, (A x B) · (A x B) = (Õ Ã)(B • B) – (A:B)2. We can treat the nabla/del operator in components as: Y H ai = o. Using this, the gradient, divergence, and curl can be expressed in index notation: Gradient: Divergence: Curl: ✓ f)' = d'f $ = 8;0') (ỹ xv)' = e' italok 1.03 Write out the Laplacian of a scalar function v2f = V . ïf in index notation and then carry out the sum. 1.04 Prove that the curl of the gradient is zero: V 1.05 Prove that the curl of the curl is given by ✓ x (ỹ x A) = 7 (7 • Ā) – V2Ā.

ansver
Answers: 2

Other questions on the subject: Mathematics

image
Mathematics, 21.06.2019 18:30, maren17
Logan wants to know how many skateboards have defective parts. he inspects 20,000 skateboards and keeps track of the number of defects per board. use his probability distribution table to find the expected value for defects on a skateboard.
Answers: 3
image
Mathematics, 21.06.2019 19:30, BaileyElizabethRay
Which graph represents the equation y =4x
Answers: 1
image
Mathematics, 21.06.2019 22:30, kacaria
Agroup of randomly selected members of the foodies food club were asked to pick their favorite type of food. the bar graph below shows the results of the survey. there are 244 members in the foodies.
Answers: 3
image
Mathematics, 21.06.2019 22:30, angeleyes4u610p6np54
Which of the following would be a reasonable estimate for the weight of a pencil? a. 1 × 10^-20 lb b. 1 × 10^20 lb c. 1 × 10^2 lb d. 1 × 10^-2 lb
Answers: 1
You know the right answer?
In lecture we introduced the Kronecker delta dij and the Levi-Civita symbol Eik which let us express...

Questions in other subjects: