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Home » The Big Reveal? When Does the PS6 Actually Drop? Find Out Fast! - Leaselab

The Big Reveal? When Does the PS6 Actually Drop? Find Out Fast! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A hydrologist is modeling groundwater flow and needs to determine the angle $\theta$ between two vectors representing water flow directions. Given vectors $\mathbf{u} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$ and $\mathbf{v} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}$, find $\cos \theta$ using the dot product.

📌 To find $\cos \theta$, we use the formula for the dot product:

📌 \mathbf{u} \cdot \mathbf{v} = \|\mathbf{u}\| \|\mathbf{v}\| \cos \theta

📌 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}

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