3. (a) Show that l₁ given by x = 3 +8 Y = 3+ s Z = -1+28 is not parallel to the line l₂: x(t) = [1, −4, −1] + t[3, -2, 1] but they do not intersect. (b) Find a non-zero vector n that is orthogonal to both lines ₁ and l2. Show that l₁ and l₂ lie in 2 parallel planes. Find general equations of the two parallel planes containing these lines. [Hint: If a line in R³ with direction vector d lies in a plane with normal vector n, then d and n must be orthogonal.]
3. (a) Show that l₁ given by x = 3 +8 Y = 3+ s Z = -1+28 is not parallel to the line l₂: x(t) = [1, −4, −1] + t[3, -2, 1] but they do not intersect. (b) Find a non-zero vector n that is orthogonal to both lines ₁ and l2. Show that l₁ and l₂ lie in 2 parallel planes. Find general equations of the two parallel planes containing these lines. [Hint: If a line in R³ with direction vector d lies in a plane with normal vector n, then d and n must be orthogonal.]
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Please see the picture for the question.
![3. (a) Show that l₁ given by
x
= 3 +8
Y
=
3+ s
Z
=
-1+28
is not parallel to the line l₂: x(t) = [1, −4, −1] + t[3, -2, 1] but they do not intersect.
(b) Find a non-zero vector n that is orthogonal to both lines ₁ and l2. Show that l₁ and l₂ lie in 2
parallel planes. Find general equations of the two parallel planes containing these lines.
[Hint: If a line in R³ with direction vector d lies in a plane with normal vector n, then d and n
must be orthogonal.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6a0ccc3-5ede-4a01-b259-12264156afc7%2F2b5d903f-9d57-472b-ae92-a5e45766dfc9%2Fcd9ye3_processed.png&w=3840&q=75)
Transcribed Image Text:3. (a) Show that l₁ given by
x
= 3 +8
Y
=
3+ s
Z
=
-1+28
is not parallel to the line l₂: x(t) = [1, −4, −1] + t[3, -2, 1] but they do not intersect.
(b) Find a non-zero vector n that is orthogonal to both lines ₁ and l2. Show that l₁ and l₂ lie in 2
parallel planes. Find general equations of the two parallel planes containing these lines.
[Hint: If a line in R³ with direction vector d lies in a plane with normal vector n, then d and n
must be orthogonal.]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education