Show that the equation of a straight line in space, represented in the Cartesian basis, is given by the following set of parametric equations: Q5: b3 X3 = (x1 – a1) + az b1 b2 X2 = - (x1 – a1) + az Where x; are the coordinates of an arbitrary point along the line, a; are the coordinates at the start of the line and b; is the coordinates corresponding to the direction that the line is parallel to. Hint: Write a vector equation that relate the position vectors x, a and b. Hence, write the equation of the straight line that starts from a = e1 + e2 + e3 parallel to b = 2e1 + e2 + 2e3. Find the coordinates where the line intersects the x1–x2, X2-X3 and x1-x3 planes.
Show that the equation of a straight line in space, represented in the Cartesian basis, is given by the following set of parametric equations: Q5: b3 X3 = (x1 – a1) + az b1 b2 X2 = - (x1 – a1) + az Where x; are the coordinates of an arbitrary point along the line, a; are the coordinates at the start of the line and b; is the coordinates corresponding to the direction that the line is parallel to. Hint: Write a vector equation that relate the position vectors x, a and b. Hence, write the equation of the straight line that starts from a = e1 + e2 + e3 parallel to b = 2e1 + e2 + 2e3. Find the coordinates where the line intersects the x1–x2, X2-X3 and x1-x3 planes.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Topic Video
Question
Both questions are required, I have my solution but only want to fact check my work.
Transcribed Image Text:Show that the equation of a straight line in space, represented in the
Cartesian basis, is given by the following set of parametric equations:
Q5:
b3
X3 =
(x1 – a1) + az
b1
b2
X2 =
- (x1 – a1) + az
Where x; are the coordinates of an arbitrary point along the line, a; are the coordinates
at the start of the line and b; is the coordinates corresponding to the direction that the
line is parallel to.
Hint: Write a vector equation that relate the position vectors x, a and b.
Hence, write the equation of the straight line that starts from a = e1 + e2 + e3 parallel
to b = 2e1 + e2 + 2e3. Find the coordinates where the line intersects the x1–x2,
X2-X3 and x1-x3 planes.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning