In R°, let L be the line spanned and oriented by v = (-1,6, 4), and let R the rotation of R° through the angle 1/2 about the v oriented line L according to the Right Hand Rule. Further, let P : R* →R° be the orthogonal projection onto the orthogonal complement of the vector n = (-6 · /53 – 56, 18 – 5 · /53, 6 · V53 – 41). Find the vector z which results from first rotating x = (6,5, -6) via R, and then projecting the rotated vector via P.
In R°, let L be the line spanned and oriented by v = (-1,6, 4), and let R the rotation of R° through the angle 1/2 about the v oriented line L according to the Right Hand Rule. Further, let P : R* →R° be the orthogonal projection onto the orthogonal complement of the vector n = (-6 · /53 – 56, 18 – 5 · /53, 6 · V53 – 41). Find the vector z which results from first rotating x = (6,5, -6) via R, and then projecting the rotated vector via P.
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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Transcribed Image Text:In IR°, let L be the line spanned and oriented by v = (-1,6, 4), and let R the rotation of R° through the angle n/2 about the v oriented line L according to the Right Hand Rule.
Further, let P : R → R* be the orthogonal projection onto the orthogonal complement of the vector n = (-6 · V53 – 56, 18 – 5 V53, 6 · V53 – 41).
Find the vector z which results from first rotatingx = (6, 5, –6) via R, and then projecting the rotated vector via P.
z =
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