Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 5: Q34E (page 264)

If the entries of two vectors $\overset{鈫�}{v}$ and $\overset{鈫�}{w}$ in $R^{n}$ are all positive, then $\overset{鈫�}{v}$ and $\overset{鈫�}{w}$ must enclose an acute angle.

Short Answer

Expert verified

The given statement is true.

Step by step solution

Acute angle

An angle that is less than $90 掳$ is called an acute angle.

check the statement

For example,

$75 掳, 45 掳, 30 掳$

All entries are positive, and their dot product will be positive,

So that,

$\overset{鈫�}{v} \overset{鈫�}{w} c o s 胃$ will also positive

Which implies that $c o s 胃$ is positive

Then $胃$ is an acute angle.

Hence, the given statement is true.

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91影视

If the entries of two vectors $\overset{鈫�}{v}$ and $\overset{鈫�}{w}$ in $R^{n}$ are all positive, then $\overset{鈫�}{v}$ and $\overset{鈫�}{w}$ must enclose an acute angle.

Short Answer

Step by step solution

Acute angle

check the statement

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91影视

If the entries of two vectors v鈫�and w鈫�in Rnare all positive, then v鈫�and w鈫�must enclose an acute angle.

Short Answer

Step by step solution

Acute angle

check the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Probability and Statistics

Logic and Functions

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

If the entries of two vectors $\overset{鈫�}{v}$ and $\overset{鈫�}{w}$ in $R^{n}$ are all positive, then $\overset{鈫�}{v}$ and $\overset{鈫�}{w}$ must enclose an acute angle.