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Initial users, \( U_0 = 50,000 \) - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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\text{proj}_{\mathbf{q}} \mathbf{p} = \frac{\mathbf{p} \cdot \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 \...
\boxed{\begin{pmatrix} 2 \\ 0 \\ -1 \end{pmatrix}}
An astrophysics researcher analyzes stellar motion with vectors $\math...

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