Let VC R³ be the plane defined by the equation 17 x+3y-12 z = 0. (a) Find a basis for V. Enter it as a list of vectors, for example (1,2,3),(4,5,6). (b) Find an orthonormal basis of V. Use exact values in your answers, for example (1/sqrt(10),3/sqrt(10),0). (c) Find the point in the plane which is nearest to the point (-2,2,0). Enter as a vector with exact values e.g. (1/10,-2/9,3/4). (d) Find the reflection of the vector (-2,2,0) in the plane V.
Let VC R³ be the plane defined by the equation 17 x+3y-12 z = 0. (a) Find a basis for V. Enter it as a list of vectors, for example (1,2,3),(4,5,6). (b) Find an orthonormal basis of V. Use exact values in your answers, for example (1/sqrt(10),3/sqrt(10),0). (c) Find the point in the plane which is nearest to the point (-2,2,0). Enter as a vector with exact values e.g. (1/10,-2/9,3/4). (d) Find the reflection of the vector (-2,2,0) in the plane V.
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:Let VC R³ be the plane defined by the equation 17 x + 3y - 12 z = 0.
(a) Find a basis for V. Enter it as a list of vectors, for example (1,2,3),(4,5,6).
(b) Find an orthonormal basis of V. Use exact values in your answers, for example (1/sqrt(10),3/sqrt(10),0).
(c) Find the point in the plane which is nearest to the point (-2,2,0). Enter as a vector with exact values e.g. (1/10,-2/9,3/4).
(d) Find the reflection of the vector (-2,2,0) in the plane V.
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