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Home » $T_n$: ending in exactly one 2 (i.e., last is 2, previous ≠ 2) - Aurero

$T_n$: ending in exactly one 2 (i.e., last is 2, previous ≠ 2) - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 = \frac{1}{2} \cdot 15 \cdot h \Rightarrow 168 = 15h \Rightarrow h = \frac{168}{15} = 11.2

📌 Thus, the shortest altitude is $ \boxed{11.2} $.Question: Find the vector $\mathbf{v}$ such that $\mathbf{v} \times \mathbf{b} = \mathbf{c} - \mathbf{b}$, where $\mathbf{b} = \langle 1, 2, 3 \rangle$ and $\mathbf{c} = \langle 4, 5, 6 \rangle$.

📌 Solution: Let $\mathbf{v} = \langle v_1, v_2, v_3 \rangle$. Compute $\mathbf{v} \times \mathbf{b}$:

📌 \mathbf{v} \times \mathbf{b} = \begin{vmatrix}

📌 \end{vmatrix} = \langle 3v_2 - 2v_3, 3v_1 - v_3, 2v_1 - v_2 \rangle.

📌 Set this equal to $\mathbf{c} - \mathbf{b} = \langle 3, 3, 3 \rangle$:

📌 3v_2 - 2v_3 = 3 \\

📌 3v_1 - v_3 = 3 \\

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