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Home » Breaking: Harry Styles’ Girlfriend Just Ditched His Boyfriend for Good—Want to Know Why? - Tacotoon

Breaking: Harry Styles’ Girlfriend Just Ditched His Boyfriend for Good—Want to Know Why? - Tacotoon

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \mathbf{v} \times \mathbf{b} = \langle v_3 \cdot 1 - v_2 \cdot 0, v_1 \cdot 0 - v_3 \cdot 0, v_2 \cdot 0 - v_1 \cdot 1 \rangle = \langle v_3, 0, -v_1 \rangle.

📌 We set this equal to \(\langle 1, 0, -1 \rangle\), resulting in the system:

📌 v_3 = 1, \quad 0 = 0, \quad -v_1 = -1.

📌 Solving gives:

📌 v_1 = 1, \quad v_2 \text{ is free}, \quad v_3 = 1.

📌 Thus, \(\mathbf{v} = \langle 1, t, 1 \rangle\) for any real \(t\).

📌 \boxed{\langle 1, t, 1 \rangle \text{ for any } t \in \mathbb{R}}

📌 Find the range of the function \( f(x) = \frac{x^2 + 1}{x^2 - 1} \) as \( x \) ranges over all real numbers such that \( x \neq \pm 1 \).

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