0. Suppose that all sides of a quadrilateral are equal in length and opposite sides are parallel. Use vector methods to show that the diagonals are perpendicular. the Cauchy-Schwarz Ing.
0. Suppose that all sides of a quadrilateral are equal in length and opposite sides are parallel. Use vector methods to show that the diagonals are perpendicular. the Cauchy-Schwarz Ing.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![60. Suppose that all sides of a quadrilateral are equal in length and
opposite sides are parallel. Use vector methods to show that the
diagonals are perpendicular.
TS,
61. Use Theorem 3 to prove the Cauchy-Schwarz Inequality:
a b ≤|a||b|
.
62. The Triangle Inequality for vectors is
|a + b | < |a| + | b|
(a) Give a geometric interpretation of the Triangle Inequality.
(b) Use the Cauchy-Schwarz Inequality from Exercise 61 to
prove the Triangle Inequality. [Hint: Use the fact that
|a + b² = (a + b) (a + b) and use Property 3 of the
dot product.]
63. The Parallelogram Law states that
|a + b ² + |a − b |² = 2|a|²+2 | b|²
1-
(a) Give a geometric interpretation of the Parallelogram Law,
(b) Prove the Parallelogram Law. (See the hint in Exercise 62.)
64. Show that if u + v and u
u and v must have the same length.
vare orthogonal, then the vectors
65. If 0 is the angle between vectors a and b, show that
projab proj, a = (a - b) cos²0
.
vectors a = (a1, a2, a3) and b = /h
To vector oth
reful to be](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa783b105-4d92-4e86-9f6d-bd566687e879%2Fd21348ef-6583-4974-9ad7-95be302f47eb%2F8h9dqio_processed.jpeg&w=3840&q=75)
Transcribed Image Text:60. Suppose that all sides of a quadrilateral are equal in length and
opposite sides are parallel. Use vector methods to show that the
diagonals are perpendicular.
TS,
61. Use Theorem 3 to prove the Cauchy-Schwarz Inequality:
a b ≤|a||b|
.
62. The Triangle Inequality for vectors is
|a + b | < |a| + | b|
(a) Give a geometric interpretation of the Triangle Inequality.
(b) Use the Cauchy-Schwarz Inequality from Exercise 61 to
prove the Triangle Inequality. [Hint: Use the fact that
|a + b² = (a + b) (a + b) and use Property 3 of the
dot product.]
63. The Parallelogram Law states that
|a + b ² + |a − b |² = 2|a|²+2 | b|²
1-
(a) Give a geometric interpretation of the Parallelogram Law,
(b) Prove the Parallelogram Law. (See the hint in Exercise 62.)
64. Show that if u + v and u
u and v must have the same length.
vare orthogonal, then the vectors
65. If 0 is the angle between vectors a and b, show that
projab proj, a = (a - b) cos²0
.
vectors a = (a1, a2, a3) and b = /h
To vector oth
reful to be
Expert Solution
Step 1
To Prove: Diagonals of given Quadrilateral is perpendicular.
Concept : We will draw a Quadrilateral on x-y axis after that we will find diagnol vectors.
Step by step
Solved in 2 steps with 1 images
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