Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
Bartleby Related Questions Icon

Related questions

Question
You are given two planes in parametric form,
x1
Il : x2
X1
IL : x2=|0 +41 2 + 2 4
X3
where
X1 , X2 , X3, 11 , d2,41, H2 E R. Let
L be the line of intersection of
п and
IL.
a. Find vectors
nj and
nɔ that are normals to
П and
IL respectively and explain how you can tell without performing any extra calculations that
II and
II, must intersect in a line.
b. Find Cartesian equations for
П and
IL.
c. For your first method, assign one of
X2 or
X3 to be the parameter
o and then use your two Cartesian equations for
П and
II, to express the other two variables in terms of
o and hence write down a parametric vector form of the line of intersection
L.
d. For your second method, substitute expressions for
X1 »
X and
X3 from the parametric form of
II, into your Cartesian equation for
II, and hence find a parametric vector form of the line of intersection
L.
e. If your parametric forms in parts (c) and (d) are different, check that they represent the same line. If your parametric forms in parts (c) and (d) are the same, explain how they could have
been different while still describing the same line.
f. Find
m = nj x n, and show that
m is parallel to the line you found in parts (c) and (d).
g. Give a geometric explanation of the result in part (f)
expand button
Transcribed Image Text:You are given two planes in parametric form, x1 Il : x2 X1 IL : x2=|0 +41 2 + 2 4 X3 where X1 , X2 , X3, 11 , d2,41, H2 E R. Let L be the line of intersection of п and IL. a. Find vectors nj and nɔ that are normals to П and IL respectively and explain how you can tell without performing any extra calculations that II and II, must intersect in a line. b. Find Cartesian equations for П and IL. c. For your first method, assign one of X2 or X3 to be the parameter o and then use your two Cartesian equations for П and II, to express the other two variables in terms of o and hence write down a parametric vector form of the line of intersection L. d. For your second method, substitute expressions for X1 » X and X3 from the parametric form of II, into your Cartesian equation for II, and hence find a parametric vector form of the line of intersection L. e. If your parametric forms in parts (c) and (d) are different, check that they represent the same line. If your parametric forms in parts (c) and (d) are the same, explain how they could have been different while still describing the same line. f. Find m = nj x n, and show that m is parallel to the line you found in parts (c) and (d). g. Give a geometric explanation of the result in part (f)
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Advanced Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Text book image
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Text book image
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Text book image
Basic Technical Mathematics
Advanced Math
ISBN:9780134437705
Author:Washington
Publisher:PEARSON
Text book image
Topology
Advanced Math
ISBN:9780134689517
Author:Munkres, James R.
Publisher:Pearson,