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what is a mangaka - Decision Point

📅 May 3, 2026 👤 scraface

May 03, 2026

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\boxed{30^\circ, 90^\circ, 150^\circ, 270^\circ}
Find the vector \(\mathbf{v}\) such that \(\mathbf{v} \times \mathbf{b...
The vector cross product \(\mathbf{v} \times \mathbf{b} = \langle v_1,...
\mathbf{v} \times \mathbf{b} = \langle v_3 \cdot 1 - v_2 \cdot 0, v_1...
We set this equal to \(\langle 1, 0, -1 \rangle\), resulting in the sy...
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}}

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