Question: Let r be a differentiable vector function of t. Show that if r (dr/dt) = 0 for all t, then |r| is constant.

Let r be a differentiable vector function of t. Show that if r ยท (dr/dt) = 0 for all t, then |r| is constant.

Step by Step Solution

★★★★★

3.34 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that r is constant given that r drdt 0 for all t we can use the chain rule of differentiatio... View full answer

blur-text-image
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 Precalculus Questions!

Q:

Provide a brief overview of a recent antitrust action that has been in the news, and assess it in the context of the Crandall & Winston paper.

Q:

Conduct a study by formulating a research question of interest to you. Briefly discuss any theory that may be relevant in addressing your research question Formulate one hypothesis statement, test...

Q:

Let r be a fixed number with | r | Converges, say with sum S. Use the properties ( of to show that And then obtain a formula for S, thus generalizing Problem 47a? (1-r)s - A

Q:

#41. I don't understand 41. Let r be a differentiable vector function of t. Show that if r . (dr dt) = 0 for all t, then r is constant. 42. Derivatives of triple scalar products

Q:

1. Let f be a differentiable scalar-valued function defined on an open subset of R". Sup- pose 5: R + R" has the property that flo(t)) = c for all t for some constant c. Prove that (1) o(t)) is...

Q:

Question 3. Consider a vector function t]. 3.1. Show that if r(t) .l. "E" for all t, then r'(t) J. 6 for all t. [2 points] 3.2. Let if = {than} be a vector. Show that if :r"(t} J. 1'! for all t? then...

Q:

how do I solve this problem? Let r() be a nice vector valued function of I variable over the real line (so that We can take the derivative of each component as many times as we want ). Show that if r...

Q:

I want some help for this q4 4. Let (X, Y) be a pair of random variables having the joint density function rs y} = (Ml11W 0. (a) Let :r be a xed constant in (1, 1). Show that given X = :r, the...

Q:

Let X NBin (r, p) with mass function (4.19) and define = r (1 p). Let r and p 1 such that stays constant. Show that X asy Poi().

Q:

Let r = (x, y, z) and e r =r/ r. Show that if a function (x, y, z) = F(r) depends only on the distance from the origin r = r= x 2 + y 2 + z 2 , then Vf = F'(r)er

Q:

Show your all calculation and also good handwriting The lower bound for the eigenvalue of the -1 matrix A = 2 -4 2 3 1 -1 o 4 3 is 4

Q:

Why is it desirable for adhesive joints to be designed so the adhesive is loaded in shear or compression?

Q:

2.1 A categorical variable has three different color codes, with the following frequencies of occurrence: Code Frequency Blue 21 Red 10 Green 19 a. Compute the percentage of values in each color...

Q:

3. Organize positive messages appropriately to build goodwill with readers

Q:

Find the indicated roots. Sketch the roots in the complex plane. The cube roots of i

Q:

Find, correct to five decimal places, the length of the side labeled x.

Q:

Sketch the graph of the set. {(x, y) | x 2 + y 2 . 4}

Q:

homework help please and thank you etlo Show Me How Calculator Print Item Activity-Based Costing for a Service Business Sterling Hotel uses activity-based costing to determine the cost of servicing...

Q:

During January, 2016, Jason Guild sells a capital asset with an adjusted cost base of $150,000 for proceeds of disposition of $220,000. He receives a down payment of $70,000 in 2016, with the balance...

Q:

Describe the Difference between Actual Assessed Value, Assessed Value, Effective Market Value, Market Value, Taxable Value and Transitional Assessed Value in New York City?