Short Answer

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

The angle $θ$ between $\vec{u}$ and $\vec{v}$ is about 97.4 $°$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Angle between two vectors

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

Is defined as:

$θ = a r c c o s (θ) = \frac{\vec{x} . \vec{y}}{| | \vec{x} | | . | | \vec{y} | |}$

Step 2: Substitute the values into the angle formula

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

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

$θ = a r c c o s (θ) = \frac{\vec{u} . \vec{v}}{| | \vec{u} | | . | | \vec{v} | |}$ .

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

Hence, the value of $θ$ is about $97.4 °$ .

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1: Angle between two vectors

Step 2: Substitute the values into the angle formula

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1: Angle between two vectors

Step 2: Substitute the values into the angle formula

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

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