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Home » ### Step 3: Compute the probability - Red Crowns

### Step 3: Compute the probability - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\mathbf{v} \times \mathbf{a} = \mathbf{b}, \quad \mathbf{v} \cdot \mat...
We use the vector triple product identity. From $ \mathbf{v} \times \m...
\mathbf{a} \times (\mathbf{v} \times \mathbf{a}) = \mathbf{a} \times \...
Using the identity $ \mathbf{a} \times (\mathbf{v} \times \mathbf{a})...
\|\mathbf{a}\|^2 \mathbf{v} = \mathbf{a} \times \mathbf{b}
Compute $ \|\mathbf{a}\|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 $
Now compute $ \mathbf{a} \times \mathbf{b} $:
\mathbf{a} \times \mathbf{b} = \begin{vmatrix}
& -2 & 1 \\
\end{vmatrix} = \mathbf{i}(2 \cdot 1 - 3 \cdot (-2)) - \mathbf{j}(1 \c...

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