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how many teaspoons in cups - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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First, compute the dot product $\mathbf{u} \cdot \mathbf{v}$:
\mathbf{u} \cdot \mathbf{v} = 3(-1) + 4(2) = -3 + 8 = 5
Next, find the magnitudes of $\mathbf{u}$ and $\mathbf{v}$:
\|\mathbf{u}\| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\|\mathbf{v}\| = \sqrt{(-1)^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}
Now, substitute these into the formula:
= 5 \cdot \sqrt{5} \cdot \cos \theta
Solve for $\cos \theta$:
\cos \theta = \frac{5}{5 \cdot \sqrt{5}} = \frac{1}{\sqrt{5}} = \frac{...
\boxed{\frac{\sqrt{5}}{5}}

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