Q68E Question: Give a geometrical des... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 1: Q68E (page 38)

Question: Give a geometrical description of the set of all vectors $\overset{鈬赌}{u} i n R^{2}$ such that $\overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w}$ .

Short Answer

Expert verified

Answer:

A geometrical description of the vectors in is, the vector is perpendicular to the vector $[\overset{鈬赌}{v} - \overset{鈬赌}{w}]$ .

Step by step solution

Consider the system

Consider the vector, $\overset{鈬赌}{u} i n {鈩�}^{2}$

Consider the condition $\overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w}$ .

Determine the geometrical description for the vector

The geometrical description is,

$\overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w} \overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w} = 0 \overset{鈬赌}{u} (. \overset{鈬赌}{u} - . \overset{鈬赌}{w)} = 0$

Where, $\overset{鈬赌}{u} (. \overset{鈬赌}{u} - . \overset{鈬赌}{w)} = 0$ represents that, the vector $\overset{鈬赌}{u}$ is perpendicular to the vector $(. \overset{鈬赌}{u} - . \overset{鈬赌}{w)}$ .

Hence, the vector $\overset{鈬赌}{u}$ is perpendicular to the vector $(. \overset{鈬赌}{u} - . \overset{鈬赌}{w)}$ . This is the geometrical description of the set of vectors $\overset{鈬赌}{u}$ in R² .

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91影视

Question: Give a geometrical description of the set of all vectors $\overset{鈬赌}{u} i n R^{2}$ such that $\overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w}$ .

Short Answer

Step by step solution

Consider the system

Determine the geometrical description for the vector

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91影视

Question: Give a geometrical description of the set of all vectorsu鈬赌inR2 such that u鈬赌.v鈬赌=u鈬赌.w鈬赌 .

Short Answer

Step by step solution

Consider the system

Determine the geometrical description for the vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Applied Mathematics

Decision Maths

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

Question: Give a geometrical description of the set of all vectors $\overset{鈬赌}{u} i n R^{2}$ such that $\overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w}$ .