Let A, B, C, D be vertices of a parallelogram with AB : D, B =...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let A, B, C, D be vertices of a parallelogram with AB : DỜ, BỜ = AD. If the distance = between A and C is equal to the distance between B and D, we claim that the parallelogram must be a rectangle. Let's show this with vectors. (a) Which pair from the following vectors must be of equal magnitude? Write the corresponding equation with the magnitude of those vectors on each side. AB, AĎ, AB + AĎ, AB – AĎ, AB + CD (b) Rewrite the equation from Part (a), using an appropriate property relating magnitude to the dot product. (c) Simplify the equation from part (b) to obtain a justification that the vertices A, B, C, D form a rectangle. Let A, B, C, D be vertices of a parallelogram with AB : DỜ, BỜ = AD. If the distance = between A and C is equal to the distance between B and D, we claim that the parallelogram must be a rectangle. Let's show this with vectors. (a) Which pair from the following vectors must be of equal magnitude? Write the corresponding equation with the magnitude of those vectors on each side. AB, AĎ, AB + AĎ, AB – AĎ, AB + CD (b) Rewrite the equation from Part (a), using an appropriate property relating magnitude to the dot product. (c) Simplify the equation from part (b) to obtain a justification that the vertices A, B, C, D form a rectangle.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics 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.
-
Cosmological redshift the expansion of the universe is often represented with a drawing like Figure a. In that figure, we are located at the symbol labeled MW (for the Milky Way galaxy), at the...
-
The site http://virtualpiano.net features an online player piano. If you click on the Key Assist menu just above the piano keyboard, and then Keyboard Keys, you will see that each key is labelled...
-
In Exercises find the derivative of the function. y = x(x + 1)
-
On January 1, 2012, Paik, Inc., borrowed $250,000 to finance the purchase of machinery. The terms of the mortgage require payments to be made at the end of every month with the first payment being...
-
On January 1, 2019, Rain Technology purchased at par $80,000, 5%, bonds of Lightyear Services Company. The bonds pay interest quarterly on March 31, June 30, September 30, and December 31. Rain...
-
What is chance in the context of a research hypothesis? And what do we do about chance in our experiments? .
-
Ten mL of pure liquid water in a cylinder with a movable piston is heated at a constant pressure of 1 atm from an initial temperature of 80?C. The temperature of the system is monitored, and the...
-
BPN Consulting Company Unadjusted Trial Balance December 31, 2023 Account Name Cash Bank Accounts Receivable Notes Receivable Debit $ 13,600 Credit 100,000 36,000 20,000 Office Supplies Prepaid...
-
Procter & Gamble has been the leading soap manufacturer in the United States since 1879, when it introduced Ivory soap. However, late in 1991, its major rival, Lever Bros. (Unilever), overtook it by...
-
One of the most popular phone accessory companies, Metlock, has a reputation for unique designs for its phone cases. Its cases fit any version of all the prominent manufacturers' phones. The...
-
In a situation of negative economic profits: a. the costs of production cannot be paid b. accounting profits are negative c. accounting profits could be positive or negative d. the firm will shut down
-
When economic profits equal zero: a. the firm should shut down b. the firm must increase profits c. the resources employed by the firm are underpaid d. resources are earning exactly what they are...
-
Economic profits are: a. accounting profits b. total revenue minus accounting costs c. total revenue minus accounting costs and opportunity costs d. total revenue minus marginal costs
-
Opportunity costs are: a. explicit costs b. the value of a resource in its current use c. implicit costs d. the value of a resource in its previous use
-
Accounting costs include all of the following except: a. electricity payment b. payment to hired workers c. how much money the operator could earn as a plumber d. fertilizer costs
-
(b) (c) After carrying out a suitable analysis, make recommendations to your client regarding which of the three pieces of investment advice he should take. (Assume a standard rate of tax of 35 %)...
-
The trade-off theory relies on the threat of financial distress. But why should a public corporation ever have to land in financial distress? According to the theory, the firm should operate at the...
-
Two dice are rolled. Given that two different numbers come up, what is the probability that one of the dice comes up 6?
-
Are low-fat diets or low-carb diets more effective for weight loss? This question was addressed in the article "Comparison of the Atkins, Zone, Ornish, and LEARN Diets for Change in Weight and...
-
A person stands on a bathroom scale. The reading is 150 lb. After the person gets off the scale, the reading is 2 lb. a. Is it possible to estimate the uncertainty in this measurement? If so,...
-
Entropy of wet steam is given by (a) \(s_{f}+x s_{f g}\) (b) \(x s_{g}\) (c) \(s_{g}+s_{f g}\) (d) \(x s_{f}\)
-
Determine the change in internal energy when one \(\mathrm{kg}\) of steam expands from \(10 \mathrm{bar} 300^{\circ} \mathrm{C}\) to 0.5 bar and 0.9 dry. Take \(c_{p s}=2.1 \mathrm{~kJ} /...
-
What do you understand by the term priming ?
Study smarter with the SolutionInn App