a If r(t) (at, bt, ct) with (a, b, c) (0, 0, 0), show that the angle between r and r ' is constant for all t 0 b If r(t) (x 0 at, y 0 bt, z 0 ct), where x 0 , y 0 , and z 0 are not all zero, show that the angle between r and r ' varies with t c Explain the results of parts (a) and (b) geometrically...

a rt rt a b ct rtr t cos 0 so cos b rt r t axo byo ...

a. If r(t) = (at, bt, ct) with (a, b, c) (0, 0, 0), show that

Question:

a. If r(t) = (at, bt, ct) with (a, b, c) ≠ (0, 0, 0), show that the angle between r and r' is constant for all t > 0.

b. If r(t) = (x₀ + at, y₀ + bt, z₀ + ct), where x₀, y₀, and z₀ are not all zero, show that the angle between r and r' varies with t.

c. Explain the results of parts (a) and (b) geometrically.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Apr 13, 2019 10:42 AM

See More Questions

(a) Use Exercise 81 to show that the angle between the tangent line and the radial line is = /4 at every point on the curve r = e6. (b) Illustrate part (a) by graphing the curve and the tangent lines...
If A ~ B, show that: (a) AT ~ BT (b) A-1 ~ B-1 (c) rA~ rB for r in R (d) An ~ Bn for n 1
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...
A random sample of 100 students was taken from a large university to study the relationship between GPA and the number of hours of study per week. The following linear regression equation was...
A bar 1 m long is bent and then stress relieved. The radius of curvature to the neutral axis is 0.50 m. The bar is 30 mm thick and is made of an elastic, perfectly plastic material with Y = 600 MPa...
On January 1, 2022, Magilla SA granted share options to officers and key employees for the purchase of 20,000 of the companys 10 par ordinary shares at 25 per share. The options were exercisable by...
An often-ignored concept in breach of contract is the availability, if any, of the award of punitive damages. Often, cases incorporate both breach of contract and tort actions. The tort actions...
Shania Twain Company was formed on December 1, 2013. The following information is available from Twains inventory records for Product BAP. A physical inventory on March 31, 2014, shows 1,600 units on...
Formulate your answer based on the information below. The intensity of care delivered dropped from a budgeted case mix of 0 . 9 0 to an actual case mix of 0 . 8 5 . What dollar effect did this have...
Bonds 1. Municipal Bonds - Municipal bonds are haircut per Exhibit 1 based on both their time to maturity and scheduled maturity at date of issue. 2. Corporate Bonds - Corporate bonds are haircut...
Suppose u and v are differentiable functions at t = 0 with u(0) = (0, 1, 1), u'(0) = (0, 7, 1), v(0) = (0, 1, 1), and v'(0) = (1, 1, 2). Evaluate the following expressions. a. b. c. (u v) dt t=0 (u...
By expressing u and v in terms of their components, prove that :(u(t) + v(t)) = u'(t) + v'(t). dt
Warren Dinner has invested in nine different investments. The returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean $500 and...
In groups of three or four, take the role of board members of a global business faced with increasingly difficult trading conditions in a country you have been operating in for some years. It is...
In a group of three or four, in the role of advisors to a developed country, you have been asked to outline some of the downsides of outward FDI. Consider the following questions and then share your...
In 2022, the top five destinations for FDI were the US, Germany, the UK, India, and China. Around 43 percent of all outbound FDI came from the US, the UK, Germany, Japan, and France. The three...
Gomez Inc. will deposit $30,000 in a 12% fund at the end of each year for 8 years beginning December 31, 2015. What amount will be in the fund immediately after the last deposit?
In May 2022, Indias commerce and industry ministry announced the highest ever FDI inflow, amounting to $83.57 billion in 202122. The key areas attracting investments were manufacturing, computer...
Distinguish between the direct and the indirect strategies. When is each appropriate?
Identify Thank You mission, strategy and core competencies. Identify strategy changes that have taken place at Thank You since its founding in 2008. Your answer must in text references and must be...
What test can be used to assess whether mean serum retinol has increased over 3 years among subjects in the vitamin A group? Ophthalmology A 5-year study among 601 participants with retinitis...
Can the test be implemented based on the data just presented? Why or why not? If yes, implement the test and report a two-tailed p-value? Ophthalmology A 5-year study among 601 participants with...
One assumption of the test in Problem 10.68 is that the distribution of serum retinol is approximately normal. To verify this assumption, the investigators obtained a frequency distribution of serum...
Brief Information: Internal auditors play a crucial role in supporting managerial decision-making within organizations. Their primary responsibility is to provide independent and objective...
Scott is a forensic accountant at a large professional services firm. He is working on an engagement at a client site and is looking at the data file containing dollar amounts on 10,000 invoices that...
The objective of the assignment is exposing the students to new sustainable technologies ( products , processes , software, etc. ) and the Life Cycle Analysis of Such technologies. The students will...

a. If r(t) = (at, bt, ct) with (a, b, c) (0, 0, 0), show that

Question:

Step by Step Answer:

a rt rt a b ct rtr t cos 0 so cos b rt r t axo byo ...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions