Respuesta :
Answer:
θ = 53.1° (to the nearest tenth)
Step-by-step explanation:
FORMULA :
Let θ be the measure of the angle between U and V :
[tex]\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }[/tex]
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[tex]\overrightarrow{U} \times \overrightarrow{V} =6\times 2+\left( -3\right) \times 1=9[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^{2}+\left( -3\right)^{2} } =\sqrt{45} =3\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^{2}+\left( 1\right)^{2} } =\sqrt{5}[/tex]
[tex]\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15[/tex]
…………………………………………………
Then
[tex]\cos \theta =\frac{9}{15} =\frac{3}{5}[/tex]
[tex]\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156[/tex]
