Q6E Find the angle胃聽between each o... [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: Q6E (page 215)

Find the angle $胃$ between each of the pairs of vectors $\overset{鈫�}{u}$ and localid="1659433601917" $\overset{鈫�}{v}$ in exercises 4 through
6. $\overset{鈫�}{u} = [\begin{matrix} 1 \\ - 1 \\ 2 \\ - 2 \end{matrix}], \overset{鈫�}{v} = [\begin{matrix} 2 \\ 3 \\ 4 \\ 5 \end{matrix}]$

Short Answer

Expert verified

The angle $胃$ between $\overset{鈫�}{u}$ and $\overset{鈫�}{v}$ is about 97.4 $掳$ .

Step by step solution

Angle between two vectors

Consider two nonzero vectors $\overset{鈫�}{x}$ and $\overset{鈫�}{y}$ in $R^{n}$ . The anglebetween these vectors

Is defined as:

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

Substitute the values into the angle formula

The given vectors are $\overset{鈫�}{u} = [\begin{matrix} 1 \\ - 1 \\ 2 \\ - 2 \end{matrix}]$ and $\overset{鈫�}{v} = [\begin{matrix} 2 \\ 3 \\ 4 \\ 5 \end{matrix}]$ .

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

$胃 = a r c c o s (胃) = \frac{\overset{鈫�}{u} . \overset{鈫�}{v}}{| | \overset{鈫�}{u} | | . | | \overset{鈫�}{v} | |}$ .

localid="1659428200763" $胃 = a r c c o s (胃) = \frac{\overset{鈫�}{u} . \overset{鈫�}{v}}{| | \overset{鈫�}{u} | | . | | \overset{鈫�}{v} | |} = a r c c o s (胃) \frac{[\begin{matrix} 1 \\ - 1 \\ 2 \\ - 2 \end{matrix}] . [\begin{matrix} 2 \\ 3 \\ 4 \\ 5 \end{matrix}]}{(\sqrt{1^{2} + {(- 1)}^{2} + 2^{2} + {(- 2)}^{1}}) (\sqrt{2^{2} + 3^{2} + 4^{2} + 5^{2}})} = a r c c o s (胃) \frac{1.2 - 1.3 + 2.4 - 2.5}{(\sqrt{1 + 1 + 4 + 4}) (\sqrt{4 + 9 + 16 + 25})} = a r c c o s (胃) \frac{2 - 3 + 8 - 10}{\sqrt{10.54}} = a r c c o s (胃) \frac{- 3}{\sqrt{540}} 鈮� 97.4 掳$

Hence, the value of $胃$ is about $97.4 掳$ .

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91影视

Find the angle $胃$ between each of the pairs of vectors $\overset{鈫�}{u}$ and localid="1659433601917" $\overset{鈫�}{v}$ in exercises 4 through
6. $\overset{鈫�}{u} = [\begin{matrix} 1 \\ - 1 \\ 2 \\ - 2 \end{matrix}], \overset{鈫�}{v} = [\begin{matrix} 2 \\ 3 \\ 4 \\ 5 \end{matrix}]$

Short Answer

Step by step solution

Angle between two vectors

Substitute the values into the angle formula

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91影视

Find the angle胃between each of the pairs of vectors u鈫�and localid="1659433601917" v鈫�in exercises 4 through 6.u鈫�=[1-12-2,v鈫�=2345]

Short Answer

Step by step solution

Angle between two vectors

Substitute the values into the angle formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Pure Maths

Mechanics Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.