Question: Let A and B be vector functions of position vector x with continuous first and second derivatives, and let F and G be scalar

Let A and B be vector functions of position vector x with continuous first and second derivatives, and let F and G be scalar functions of position x with continuous first and second derivatives. Use index notation to show that: (a) V. (VxA)-0. (b) x (VF) = 0. (c) V (VFx VC) -0. (d) V (FA)-A.VF+FV.A.

Step by Step Solution

★★★★★

3.43 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The b If position vector 2 iti A Where V VXA VV v 1 24 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Let A and B be any two events defined on S. Suppose that P (A) = 0.4, P(B) = 0.5, and P (A B) = 0.1. What is the probability that A or B but not both occur?

Let A and B be two events defined on S. If the probability that at least one of them occurs is 0.3 and the probability that A occurs but B does not occur is 0.1, what is P (B)?

Let a and b be nonzero vectors in Rn. a) If (t) = a + tb for t R, show that for each to, t0, t1, t2 R with t1, t2 t0, the angle between (t0) - (t0) - (t0) and (t2) - (t0) is 0 or . b) If is the...

Given a vector x Rn+l, the (n + l) Ã (n + l) matrix V defined by is called the Vandermonde matrix. (a) Show that if Vc = y and p(x) = c1 + c2x + ... + cn+1xn then p(xi) = yi, i = 1, 2, ..., n...

Write a MATLAB program that generates and graphs the noisy cosine sample paths Xcc(t), Xdc(t), Xcd(t), and Xdd(t) of Figure 13.3. Note that the mathematical definition of Xcc(t) is Xcc(t) = 2cos(2t)...

4.35. (Sec. 4.4) Prove that conditional on ZI" = ZI,,' a = 1, ... , n, RZ /0 - RZ) is distributed like T 2/(N* - 1), where T Z = N* i' S-I i based on N* = n observations on a vector X with p* = p - 1...

Problem 4.17 The data to be used in this problem are contained in the S-Plus script file crude.asc. Running this script will create the data frame CRUDE containing a numerical matrix with 3325 rows...

Let C be the curve obtained by intersecting a cylinder of radius r and a plane. Insert two spheres of radius r into the cylinder above and below the plane, and let F 1 and F 2 be the points where the...

=+14. Let x be the standard Euclidean norm of a vector x Rn. A vector x with x = 1 is said to be a unit vector. For any sequence x1,...,xn of n unit vectors from Rn, it is possible to find n numbers...

1.13 To see that Theorem 1.1 is not necessarily valid without boundedness of the fourth (or some higher) derivative, suppose that the Xs are distributed as N(,2) and let h(X) = ex4 . Then, all...

Check IF all journal entries have been entered correctly. Correct the journal entries WHERE applicable. Are all journal entries from june 1 to june 30? 1.Purchase Invoice #BH-5621 Dated June 2,...

Construct motion diagrams showing the velocity and acceleration of a projectile at several points along its path if (a) The projectile is launched horizontally and (b) The projectile is launched at...

Determine if the series n = 1 1 ( 2 n + 3 ) 2 converges or diverges by: The limit comparison test.

These financial statement items are for Delta Corporation at year-end, July 31, 2020. SHOW YOUR WORK. Salaries and wages payable $ 2,080 Salaries and wages expense 57,500 Supplies expense 17,600...

Consider the reaction: H 2 (g) + 2 ICl (g) I 2 (g) + 2 HCl (g) The observed rate law is Rate = k [H 2 ][ICl] . A proposed mechanism for this reaction is: Step 1: H 2 (g) + ICl (g) HI (g) + HCl (g)...

The graph represents the electromotive force (emf) generated in the dynamo coil, time for revolving, starting from normal position till (emf) becomes -50V for the first time equals: (A) 50 msec (V)...

Define the design thinking in food delivery application in innovation strategies

The broadcast address of 205.169.179.219/27 a O 205.169.179.24 .b O 205.169.179.22. .c O 205.169.179.25 d O 205.169.179.22

Operations and supply chain processes can be conveniently categorized as all but which of the following? Option A Selling Option B Planning Option C Making Option D Delivering

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

A network based service manages persistent objects. The service must enforce an access control policy to protect the objects. (a) Discuss how this access control might best be implemented for the...

Please use C++ for this program. Please read the problem and follow the instruction in main.cpp for this program. Problem: - Design an abstract class called Shape: - Private variables double x and...

Miller-Rabin test to check whether a number N is composite. This will involve computing a N1 mod N for some value of a. [10 marks] Carry out the steps for N = 65 and a = 1, 2, 8 and 12. on what each...

For each of the following definitions, give the type of the function and its arguments. If there is a type mismatch, you should explain the reason for the mismatch. Note that for recursive functions,...