Answered: Given is the plane V : a · x = 9 with a…

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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Question

the following question is from linear algebra= Given is the plane V : a · x = 9 with a = (2, -3,6)t. Calculate the distance from O= (0,0,0) and P=(1,-2,-1) to V.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution

Step 1: Introduction

Given that:

The Plane $V colon a x equals 9$ with $a equals open parentheses 2 comma negative 3 comma 6 close parentheses to the power of T$

To find: The distance from $O open parentheses 0 comma 0 comma 0 close parentheses$ and $P open parentheses 1 comma negative 2 comma negative 1 close parentheses$ to V.

Concept:

The distance d between a point $P subscript 0 open parentheses x subscript 0 comma y subscript 0 comma z subscript 0 close parentheses$ and a plane with the equation $A x plus B y plus C z plus D equals 0$ is given by:

$d equals fraction numerator open vertical bar A x subscript 0 plus B y subscript 0 plus C z subscript 0 plus D close vertical bar over denominator square root of A squared plus B squared plus C squared end root end fraction$