Short Answer

Find the angle $θ$ between each of the pairs of vectors $\overset{⇀}{u}$ and $\overset{⇀}{v}$ in exercises 4 through 6.
4. $\overset{⇀}{u} = [\begin{matrix} 1 \\ 1 \end{matrix}], \overset{⇀}{v} = [\begin{matrix} 7 \\ 11 \end{matrix}] .$

The angle $θ$ between $\overset{⇀}{u}$ and $\overset{⇀}{v}$ is about $12.58 °$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Angle between two vectors

Consider two nonzero vectors $\overset{⇀}{x}$ and role="math" localid="1659434098948" $\overset{⇀}{y}$ in $R^{n}$ . The angle between these vectors

Is defined as:

role="math" localid="1659434271678" $θ = a r c c o s \frac{\overset{⇀}{x} . \overset{⇀}{y}}{|| \overset{⇀}{x} || . || \overset{⇀}{y} ||}$

Step 2: Substitute the values into the angle formula

$θ = a r c c o s \frac{\overset{⇀}{u} . \overset{⇀}{v}}{|| \overset{⇀}{u} || . || \overset{⇀}{v} ||} = a r c c o s \frac{[[11] [\begin{matrix} 7 \\ 11 \end{matrix}]]}{(\sqrt{1 - 1 + 1 - 1}) (\sqrt{7 - 7 + 11 - 11})} = a r c c o s \frac{1 - 7 + 1 - 11}{(\sqrt{1 + 1}) (\sqrt{49 + 121})} = a r c c o s \frac{18}{\sqrt{340}} = a r c c o s \frac{18}{18.44} = a r c c o s (0.976) \approx 12.58 °$

Hence, the value of $θ$ is about $12.58 °$ .

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Linear Algebra With Applications

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Short Answer

Find the angle $θ$ between each of the pairs of vectors $\overset{⇀}{u}$ and $\overset{⇀}{v}$ in exercises 4 through 6.
4. $\overset{⇀}{u} = [\begin{matrix} 1 \\ 1 \end{matrix}], \overset{⇀}{v} = [\begin{matrix} 7 \\ 11 \end{matrix}] .$

Step by Step Solution

Step 1: Angle between two vectors

Step 2: Substitute the values into the angle formula

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Linear Algebra With Applications

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Short Answer

Find the angle θ between each of the pairs of vectors u⇀ and v⇀ in exercises 4 through 6.4. u⇀=[11],v⇀=[711] .

Step by Step Solution

Step 1: Angle between two vectors

Step 2: Substitute the values into the angle formula

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Pure Maths

Find the angle $θ$ between each of the pairs of vectors $\overset{⇀}{u}$ and $\overset{⇀}{v}$ in exercises 4 through 6.
4. $\overset{⇀}{u} = [\begin{matrix} 1 \\ 1 \end{matrix}], \overset{⇀}{v} = [\begin{matrix} 7 \\ 11 \end{matrix}] .$