Question

Find the measure of the angle between u = 6i - 3j and
v = 2i+j to the nearest tenth of a degree.

Answer 1

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 :

$\cos \theta =\frac{\overrightarrow{U} .\overrightarrow{V} }{\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert }$

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

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

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

$\left\Vert \overrightarrow{U} \right\Vert \times \left\Vert \overrightarrow{V} \right\Vert =3\sqrt{5} \times \sqrt{5} = 15$

…………………………………………………

Then

$\cos \theta =\frac{9}{15} =\frac{3}{5}$

$\theta =\cos^{-1} \left( \frac{3}{5} \right) =53.130102354156$