The Law of Cosines: Prove that the formula ||v - w||2 = ||v||2 + ||w||2 - 2
Question:
||v - w||2 = ||v||2 + ||w||2 - 2 ||v|| ||w|| cosθ, (3.21)
where θ is the angle between v and w, is valid in any inner product space.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (9 reviews)
Using 320 v w 2 ...View the full answer
Answered By
Jonas Araujo
I have recently received the degree of PhD. In Physics by the Universidade Federal do Maranhão after spending a term in Durham University, as I have been awarded a scholarship from a Brazilian mobility program. During my PhD. I have performed research mainly in Theoretical Physics and published works in distinguished Journals (check my ORCID: https://orcid.org/0000-0002-4324-1184).
During my BSc. I have been awarded a scholarship to study for a year in the University of Evansville, where I have worked in detection-analysis of photon correlations in the the Photonics Laboratory. There I was a tutor in Electromagnetism, Classical Mechanics and Calculus for most of that year (2012).
I am very dedicated, honest and a fast learner, but most of all, I value a job well done.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Use the Law of Cosines to prove the identity a + b? + c? 2abc cos A cos B b cos C
-
Use the Law of Sines and the Law of Cosines to find all of the missing side lengths and angle measures. a. b. 87 51 10 m 3 eni 82 2.3 cm CIn
-
1. The standard form of the Law of Cosines for cos B = a2 + c2 b2 / 2ac is ________. 2. When solving an oblique triangle given three sides, use the ________ form of the Law of Cosines to solve for...
-
The Depression Anxiety Stress Scales (DASS) is a tool to measure the depression, anxiety and stress levels of individuals. For measuring the stress level, the DASS score ranges from 0 to 42 and a...
-
Raquel is concerned with efficiency. She believes it is probably more efficient to use SPT (shortest processing time) as her priority rule. (a) Develop a sequence using SPT based on processing time...
-
What is the resistance of an automobile headlight through which 2.50 A flows when 12.0 V is applied to it? Strategy We can rearrange Ohm's law as stated by I = V/R and use it to find the resistance.
-
About 83% of U.S. employees drive their own vehicle to work. You randomly select a sample of U.S. employees. Find the probability that more than 100 of the employees drive their own vehicle to work....
-
Corbertt Pharmaceuticals manufactures an over-the-counter allergy medication. The company sells both large commercial containers of 1,000 capsules to health-care facilities and travel packs of 20...
-
Please calculate these two quesitions,thanks. J L Question One. Using the following table, how would you carry out the covered interest arbitrage in the case? Show all the steps and determine the...
-
This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate R bps....
-
Prove that (ai + a2 +....... + an)2 n(a21 + a22 + .......+ a2n) for any real numbers a\..........a". When does equality hold?
-
Explain why the inequality (v, w) < ||v|| ||w||, obtained by omitting the absolute value sign on the left hand side of Cauchy-Schwarz, is valid.
-
How would you describe economic rent in the case of a movie star earning millions of dollars each year?
-
What is the basis of ethnonationalist movements today?
-
How does the anatomy of early monkeys and apes differ, and what do the shifts in their relative abundance suggest about the selective pressures acting on each group?
-
What do the three main lines of evidence suggest about models for modern human origins?
-
Suppose the government reduces taxes by 2 billion, that there is no crowding out and that the MPC is 0.75. a. What is the initial effect of the tax reduction on AD? b. What additional effects follow...
-
Why do you think a society would have marriage rules such as the levirate and sororate?
-
Calculate the volume of the composite shapes in Questions. 4cm 6cm 2 cm 2 cm 8cm 6 cm
-
A heat engine has a heat input of 3 Ã 104 Btu/h and a thermal efficiency of 40 percent. Calculate the power it will produce, in hp. Source 3 x 10 Btu/h 40% HE Sink
-
Let A be an m n matrix with singular value decomposition UVT, and suppose that A has rank r, where r < n. Show that {v1, ..., vr} is an orthonormal basis for R(AT).
-
Let A be an n n matrix. Show that ATA and AAT are similar.
-
Show that if is a singular value of A then there exists a nonzero vector x such that = ||Ax||2 / ||x||2
-
"Ecommerce is the newest and most disruptive distribution channel wherein 1 po goods and services are represented virtually online and then distributed directly to the buyer" Agree Disagree
-
1) What is the system and service manager on our Fedora VMs?How can you verify that on your system? (show the command below).What version of Linux is running on fawad, and what is it's system...
-
7)The terminal value is always "placed" in the last year of a DCF forecast. If the terminal value is placed in year 2024 (as it is in Case 2, for P&G), this value represents...
Study smarter with the SolutionInn App