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Home » Plugging in $ s = 120 $ meters and $ t = 15 $ seconds: - DNSFLEX

Plugging in $ s = 120 $ meters and $ t = 15 $ seconds: - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 \text{proj}_{\mathbf{q}} \mathbf{p} = \frac{\mathbf{p} \cdot \mathbf{q}}{\|\mathbf{q}\|^2} \mathbf{q}

📌 First, compute the dot product:

📌 \mathbf{p} \cdot \mathbf{q} = 4(2) + (-1)(0) + 3(-1) = 8 + 0 - 3 = 5

📌 Next, find $\|\mathbf{q}\|^2$:

📌 \|\mathbf{q}\|^2 = 2^2 + 0^2 + (-1)^2 = 4 + 0 + 1 = 5

📌 Now compute the scalar multiplier:

📌 \frac{5}{5} = 1

📌 \text{proj}_{\mathbf{q}} \mathbf{p} = 1 \cdot \begin{pmatrix} 2 \\ 0 \\ -1 \end{pmatrix} = \begin{pmatrix} 2 \\ 0 \\ -1 \end{pmatrix}

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