Let v (x, y) and Prove that the angle between v and v is Ve (x cos 0 y sin 0, x sin 0 y cos 0)...

That is The dot product of the vectors v and ve is v Ve x y x cos 0 y sin 0 ...

Let v = (x, y) and Prove that the angle between v and v is .

Question:

Let v = (x, y) and

Ve = (x cos 0 + y sin 0, -x sin 0 + y cos 0)

Prove that the angle between v and v_θis θ.

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 31, 2023 04:28 AM

See More Questions

Let x and y be vectors in Rn and let Q be an n x n orthogonal matrix. Show that if z = Qx and w = Qy then the angle between z and w is equal to the angle between x and y.
Let Q be an orthogonal 2 ( 2 matrix and let x and y be vectors in. If ( is the angle between x and y, prove that the angle between Qx and Qy is also (. (This proves that the linear transformations...
Let u and v be nonzero vectors in R". In Section 5.3 we defined the angle between u and v to be the angle Î¸ such that A linear operator L: Rn Rn is called angle preserving if the angle...
On January 2, 2016, Allen Company purchased a machine for $70,000. This machine has a five-year useful life, a residual value of $10,000, and it is depreciated using the straight-line method for...
A 65-kg airplane pilot pulls out of a dive by following the arc of a circle whose radius is 300 m. At the bottom of the circle, where her speed is 180 km/h, (a) What are the direction and magnitude...
If the later flight was actually the next day (and the airline offered you an accommodation voucher along with the meal vouchers) and you would be late getting into work, would you make the same...
Describe the significance of constraints and how they relate to business rules.
Consider a rod of diameter D, thermal conductivity k, and length 2L that is perfectly insulated over one portion of its length, - L
Use conducted values for a company/industry of your choosing, and estimate customer lifetime value (CLV). Please provide step by step calculation information. Use these formulas and show the work of...
Let v be a nonzero vector. The angles , , between v and the unit vectors i, j, k are called the direction angles of v (Figure 30). The cosines of these angles are called the direction cosines of v....
In this exercise, we prove the CauchySchwarz inequality: If v and w are any two vectors, then |vw| ||v||||w|| . |xv +w||2 for x a scalar. Show that f(x) = ax + bx+c, where a = (a) Let f(x) = c =...
Rudy Co. has total fixed costs of $520,000. A unit of product sells for $15 and variable costs per unit are $11 a) Prepare a contribution margin income statement showing predicted net income (loss)...
Suppose that we want to write down a string of three letters in alphabetical order, where we can repeat letters. So AAA. EEL. and XYZ are all valid, but CAT, ZYX and ELE are not. Suppose that someone...
Show that for every n N, we have 2" > n. b) Deduce that if S be a subset of IN with the following properties i) 2 S for every n N ii) If n S for some n 2 then n - 1 S, then S = N. c) Show that 1 + 2...
Consider the following function: (0 for t-2 -4-2t for-2t0 x(t)=-4+3t for 0t4 16-21 for 418 0 for t8 a) Sketch the function x(t) b) Sketch the function 3x(t+1) c) Sketch the function (1/2)x(3+) d)...
Project planners have sought the judgment of various knowledgeable engineers, vendors, and foremen and have developed the time estimates for the plant construction project as shown in the table...
We are given a function f : X Y a) Show that for all sets G, H C Y we have i) f- (GUH) = (G) u (H), and ii) (G ^ H) = -(G)n f(H). b) Show that for A, B C X, we have i) f(AUB) = f(A) U f(B) and ii)...
List five characteristics of customers that are high cost-to-serve customers. List five characteristics of customers that are low cost-to-serve customers.
Determine which of the following limits exist. Compute the limits that exist. lim x-0 1- + 3x X
Establish identity. tan + cot = sec csc
Establish identity.
Establish identity.
The following events occurred for Johnson Company: Received investment of cash by organizers and distributed to them 1 , 1 9 0 shares of $ 1 par value common stock with a market price of $ 2 0 per...
Adams Camps, Incorporated leases the land on which it builds camp sites. Adams is considering opening a new site on land that requires $ 4 , 3 5 0 of rental payment per month. The variable cost of...
artnership Income Allocation Various Options The January 1 , 2 0 1 7 , balance sheet of the partnership of Linda Kingston and Jeannette Allen is shown below. Assets Liabilities and Capital Cash $ 2 0...

Let v = (x, y) and Prove that the angle between v and v is .

Question:

Ve= (x cos 0 + y sin 0, -x sin 0 + y cos 0)

Step by Step Answer:

That is The dot product of the vectors v and ve is v Ve x y x cos 0 y sin 0 ...View the full answer

Calculus

Students also viewed these Mathematics questions