Q5E Find the angle聽胃 between each ... [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 5: Q5E (page 215)

Find the angle $胃$ between each of the pairs of vectors $\overset{鈫�}{u}$ and in exercises 4 through 6.
5. $\overset{鈫�}{u} = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}| \overset{鈫�}{V} = [\begin{matrix} 2 \\ 3 \\ 4 \end{matrix}]$ .

Short Answer

Expert verified

The angle $胃$ between $\overset{鈫�}{u}$ and $\overset{鈫�}{v}$ is about 0.1 2 1 9 radians.

Step by step solution

Correlation coefficient

The correlation coefficientrbetween two characteristics of a population is the

Cosine of the angle between the deviation vectors $\overset{鈫�}{x}$ and $\overset{鈫�}{y}$ for the two characteristics:

$r = c o s (胃) = \frac{\overset{鈫�}{x} . \overset{鈫�}{y}}{| | \overset{鈫�}{x} | | . | | \overset{鈫�}{y} | |}$

Step 2: Substitute the values into the angle formula

The given vectors are $\overset{鈫�}{u} = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$ and $\overset{鈫�}{v} = [\begin{matrix} 2 \\ 3 \\ 4 \end{matrix}]$ .

The angle formula role="math" localid="1659426804326" $胃 = c o s^{- 1} = \frac{\overset{鈫�}{x} . \overset{鈫�}{y}}{| | \overset{鈫�}{u} | | . | | \overset{鈫�}{v} | |}$ .

Find $\overset{鈫�}{u} . \overset{鈫�}{v}$ and $| | \overset{鈫�}{u} | | . | | \overset{鈫�}{v} | |$

$\overset{鈫�}{u} . \overset{鈫�}{v} = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}] . [\begin{matrix} 2 \\ 3 \\ 4 \end{matrix}] = 1 脳 2 + 3 + 3 脳 4 = 20$

$| | \overset{鈫�}{u} | | = \sqrt{1^{2} + 2^{2} + 3^{2}} 鈬� \sqrt{14} | | \overset{鈫�}{v} | | = \sqrt{2^{2} + 3^{2} + 4^{2}} 鈬� \sqrt{29}$

Now, calculate the angle by substituting the required values into the angle formula.

$\begin{array}{l} 胃 = \cos^{- 1} \frac{20}{\sqrt{14} . \sqrt{29}} \\ 鈮� 0.1219 \end{array}$

Hence, the value of $胃$ is about $0.1219$ radians.

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91影视

Find the angle $胃$ between each of the pairs of vectors $\overset{鈫�}{u}$ and in exercises 4 through 6.
5. $\overset{鈫�}{u} = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}| \overset{鈫�}{V} = [\begin{matrix} 2 \\ 3 \\ 4 \end{matrix}]$ .

Short Answer

Step by step solution

Correlation coefficient

Step 2: Substitute the values into the angle formula

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Most popular questions from this chapter

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91影视

Find the angle胃 between each of the pairs of vectorsu鈫� and in exercises 4 through 6.5.u鈫�=[123V鈫�=234] .

Short Answer

Step by step solution

Correlation coefficient

Step 2: Substitute the values into the angle formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Pure Maths

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the angle $胃$ between each of the pairs of vectors $\overset{鈫�}{u}$ and in exercises 4 through 6.
5. $\overset{鈫�}{u} = [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}| \overset{鈫�}{V} = [\begin{matrix} 2 \\ 3 \\ 4 \end{matrix}]$ .