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Exercise 6.11 In A³ consider the lines : { x + y = (x + 1)² + 1 = 0 x z = 0 Tk: x=t+2 y = 3-t z=-t-2. a) Determine, if they exist, values of k such that the line r is orthogonal to the line s. b) For all the lines r found in a), check if there exists a plane containing the lines 7 and s and, if so, write the equations of this plane. c) Determine, if they exist, the values of k such that the line r is parallel to the line s.

Exercise 6.11 In A³ consider the lines : { x + y = (x + 1)² + 1 = 0 x z = 0 Tk: x=t+2 y = 3-t z=-t-2. a) Determine, if they exist, values of k such that the line r is orthogonal to the line s. b) For all the lines r found in a), check if there exists a plane containing the lines 7 and s and, if so, write the equations of this plane. c) Determine, if they exist, the values of k such that the line r is parallel to the line s.

Advanced Engineering Mathematics
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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Exercise 6.11 In A³ consider the lines : { x + y = (x + 1)² + 1 = 0 x+z=0 Tk: x=t+2 y=3-t z=-t-2. a) Determine, if they exist, values of k such that the line r is orthogonal to the line s. b) For all the lines r found in a), check if there exists a plane containing the lines r and s and, if so, write the equations of this plane. c) Determine, if they exist, the values of k such that the line r is parallel to the line s. d) For all the lines found in c), compute the distance between r and s.
Transcribed Image Text:Exercise 6.11 In A³ consider the lines : { x + y = (x + 1)² + 1 = 0 x+z=0 Tk: x=t+2 y=3-t z=-t-2. a) Determine, if they exist, values of k such that the line r is orthogonal to the line s. b) For all the lines r found in a), check if there exists a plane containing the lines r and s and, if so, write the equations of this plane. c) Determine, if they exist, the values of k such that the line r is parallel to the line s. d) For all the lines found in c), compute the distance between r and s.
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