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Home » Emo Life Revealed: What It Really Means Beyond the Fashion Statement! - Blask

Emo Life Revealed: What It Really Means Beyond the Fashion Statement! - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Find the vector \(\mathbf{v}\) such that \(\mathbf{v} \times \mathbf{b} = \langle 1, 0, -1 \rangle\) and \(\mathbf{b} = \langle 0, 1, 0 \rangle\).

📌 The vector cross product \(\mathbf{v} \times \mathbf{b} = \langle v_1, v_2, v_3 \rangle \times \langle 0, 1, 0 \rangle\) is computed as:

📌 \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 \(t\).

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