This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry. (a) Let u and v be two nonzero vectors in R². Suppose that Ju| = |v| = |u + v| products to find the angle between u and v. 1. Use dot Hint: Note that |u|? = |v|² = |u + v]? = (u + v)·(u+ v). (b) Draw a picture illustrating what you found. (c) Use the idea you developed in part (a) and (b) to prove the following proposition: "A parallelogram is a rhombus if and only if its diagonals meet at a right angle."
This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry. (a) Let u and v be two nonzero vectors in R². Suppose that Ju| = |v| = |u + v| products to find the angle between u and v. 1. Use dot Hint: Note that |u|? = |v|² = |u + v]? = (u + v)·(u+ v). (b) Draw a picture illustrating what you found. (c) Use the idea you developed in part (a) and (b) to prove the following proposition: "A parallelogram is a rhombus if and only if its diagonals meet at a right angle."
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3. This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry.
|v| = |u+v]
1. Use dot
(a) Let u and v be two nonzero vectors in R². Suppose that u
products to find the angle between u and v.
Hint: Note that |u|? = |v[² = |u + v[? = (u + v) · (u + v).
(b) Draw a picture illustrating what you found.
(c) Use the idea you developed in part (a) and (b) to prove the following proposition:
"A parallelogram is a rhombus if and only if its diagonals meet at a right angle."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F153f7311-79ea-4d70-a40c-822c1ada8bcd%2Fbfd10fdf-8696-4f5d-bb22-2dfb9624813f%2Fsq5cefj_processed.png&w=3840&q=75)
Transcribed Image Text:3. This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry.
|v| = |u+v]
1. Use dot
(a) Let u and v be two nonzero vectors in R². Suppose that u
products to find the angle between u and v.
Hint: Note that |u|? = |v[² = |u + v[? = (u + v) · (u + v).
(b) Draw a picture illustrating what you found.
(c) Use the idea you developed in part (a) and (b) to prove the following proposition:
"A parallelogram is a rhombus if and only if its diagonals meet at a right angle."
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