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palo alto california weather forecast - Feedz API

📅 May 18, 2026 👤 scraface

May 18, 2026

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So, the total area of the hexagon is:
Thus, the area of the active zone is:
The bases are excluded, so no base area is included.
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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...
The area is the magnitude of the cross product $\mathbf{r} \times \mat...

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