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Home » #### 1,157.63 (rounded to two decimal places) - go-checkin.com

#### 1,157.63 (rounded to two decimal places) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: Find the vector $\mathbf{v}$ that satisfies $\mathbf{v} imes \mathbf{a} = \mathbf{b}$, where $\mathbf{a} = \langle 1, 2, 3

📌 angle$ and $\mathbf{b} = \langle 4, 5, 6

📌 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:

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