Let VcR be the plane defined by the equation 17 x-3 y- 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 (1,2,0). Enter as a vector with exact values e.g. (1/10,-2/9,3/4).

Let VcR be the plane defined by the equation 17 x-3 y- 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 (1,2,0). Enter as a vector with exact values e.g. (1/10,-2/9,3/4).

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let VcR be the plane defined by the equation 17 x - 3 y – 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 (1,2,0). Enter as a vector with exact values e.g. (1/10,-2/9,3/4).
(d) Find the reflection of the vector (1,2,0) in the plane V.

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