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Unlock Exclusive Live Features on Xbox – Live For Xbox, Now Available! - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 5Question: Find the vector $\mathbf{v}$ such that $\mathbf{v} \times \mathbf{a} = \mathbf{b}$ and $\mathbf{v} \cdot \mathbf{a} = 0$, where $\mathbf{a} = \langle 1, 2, 3 \rangle$ and $\mathbf{b} = \langle 4, 5, 6 \rangle$.

📌 Solution: Let $\mathbf{v} = \langle v_1, v_2, v_3 \rangle$. The cross product $\mathbf{v} \times \mathbf{a} = \mathbf{b}$ gives:

📌 \begin{vmatrix}

📌 \mathbf{i} & \mathbf{j} & \mathbf{k} \\

📌 v_1 & v_2 & v_3 \\

📌 & 2 & 3 \\

📌 \end{vmatrix} = \langle 2v_3 - 3v_2, 3v_1 - v_3, v_2 - 2v_1 \rangle = \langle 4, 5, 6 \rangle.

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