Find the angle, $α$ , between the vectors.
$\begin{array}{l} \vec{u} = ⟨ - 2, 3 ⟩ \\ \vec{w} = ⟨ 4, - 2 ⟩ \end{array}$

Answer

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Answer

$α = \cos^{- 1} (\frac{- 14}{\sqrt{13} \sqrt{20}})$

Steps

Step 1 ： $\cos α = \frac{\vec{u} \cdot \vec{w}}{| | \vec{u} | | | | \vec{w} | |}$

Step 2 ： $\cos α = \frac{(- 2) (4) + (3) (- 2)}{\sqrt{(- 2)^{2} + 3^{2}} \sqrt{4^{2} + (- 2)^{2}}}$

Step 3 ： $α = \cos^{- 1} (\frac{- 14}{\sqrt{13} \sqrt{20}})$