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when does mcdonald's start serving breakfast - DevRocket

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Solution: The vector equation $\mathbf{v} imes \mathbf{a} = \mathbf{b}$ has a solution only if $\mathbf{a} \cdot \mathbf{b} = 0$, since the cross product is perpendicular to $\mathbf{a}$.

📌 \mathbf{a} \cdot \mathbf{b} = 1(4) + 2(5) + 3(6) = 4 + 10 + 18 = 32

📌 Since the dot product is not zero, there is **no** vector $\mathbf{v}$ such that $\mathbf{v} imes \mathbf{a} = \mathbf{b}$. The equation is inconsistent.

📌 oxed{ ext{No such vector } \mathbf{v} ext{ exists}}

📌 Question: Find all angles $z \in [0^\circ, 360^\circ]$ that satisfy $\sin(2z) = \cos(z)$.

📌 Solution: Use identity $\sin(2z) = 2\sin z \cos z$. So:

📌 2\sin z \cos z = \cos z.

📌 2\sin z \cos z - \cos z = 0 \Rightarrow \cos z (2\sin z - 1) = 0.

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