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Consider a hyperplane H = {(w, x, y, z) E R4 | 2w + 3x - 4y + z = 10} and a line ((t) (1,-1,1,-1) +t(3, -2, 1, 4) in R¹. (a) Show that H and (t) are parallel and disjoint. (b) Compute the distance between H and ((t). (c) Find the equation of the line L(t) that goes through the point X(1,2, 1.4) and is per- pendicular to H. Find where this line intersects H. (d) Use (c) to find the distance between H and the point X (1, 2, 1,4).

Consider a hyperplane H = {(w, x, y, z) E R4 | 2w + 3x - 4y + z = 10} and a line ((t) (1,-1,1,-1) +t(3, -2, 1, 4) in R¹. (a) Show that H and (t) are parallel and disjoint. (b) Compute the distance between H and ((t). (c) Find the equation of the line L(t) that goes through the point X(1,2, 1.4) and is per- pendicular to H. Find where this line intersects H. (d) Use (c) to find the distance between H and the point X (1, 2, 1,4).

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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Consider a hyperplane H = {(w,x, y, z) € R¹|2w + 3x - 4y + z = 10} and a line (t) = (1,-1, 1,-1) + t(3, -2, 1,4) in R¹. (a) Show that H and (t) are parallel and disjoint. (b) Compute the distance between H and l(t). (c) Find the equation of the line L(t) that goes through the point X(1,2,1,4) and is per- pendicular to H. Find where this line intersects H. (d) Use (c) to find the distance between H and the point X(1, 2, 1,4).
Transcribed Image Text:Consider a hyperplane H = {(w,x, y, z) € R¹|2w + 3x - 4y + z = 10} and a line (t) = (1,-1, 1,-1) + t(3, -2, 1,4) in R¹. (a) Show that H and (t) are parallel and disjoint. (b) Compute the distance between H and l(t). (c) Find the equation of the line L(t) that goes through the point X(1,2,1,4) and is per- pendicular to H. Find where this line intersects H. (d) Use (c) to find the distance between H and the point X(1, 2, 1,4).
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