Question

Find the measure of the angle between u = 6i - 3j and

v = 2i+j to the nearest tenth of a degree.

Answer 1

θ = 53.1° (to the nearest tenth)

Explanation:

FORMULA :

Let θ be the measure of the angle between U and V :

`\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert * \left\Vert \overrightarrow{V} \right\Vert }`

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`\overrightarrow{U} * \overrightarrow{V} =6* 2+\left( -3\right) * 1=9`

`\left\Vert \overrightarrow{U} \right\Vert =\sqrt{6^(2)+\left( -3\right)^(2) } =√(45) =3√(5)`

`\left\Vert \overrightarrow{U} \right\Vert =\sqrt{2^(2)+\left( 1\right)^(2) } =√(5)`

`\left\Vert \overrightarrow{U} \right\Vert * \left\Vert \overrightarrow{V} \right\Vert =3√(5) * √(5) = 15`

…………………………………………………

Then

`\cos \theta =(9)/(15) =(3)/(5)`

`\theta =\cos^(-1) \left( (3)/(5) \right) =53.130102354156`