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Home » Why This Pensar Conjugation Rule Will Change Your Spanish Forever! - Simpleprint

Why This Pensar Conjugation Rule Will Change Your Spanish Forever! - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 $\sin z = \frac{1}{2} \Rightarrow z = 30^\circ, 150^\circ$

📌 Thus, the solutions are:

📌 \boxed{30^\circ, 90^\circ, 150^\circ}

📌 Question: Find the value of $x$ so that the vectors $\begin{pmatrix} 2 \\ x \\ 3 \end{pmatrix}$ and $\begin{pmatrix} x \\ -1 \\ 4 \end{pmatrix}$ are orthogonal.

📌 Two vectors are orthogonal if their dot product is zero:

📌 \begin{pmatrix} 2 \\ x \\ 3 \end{pmatrix} \cdot \begin{pmatrix} x \\ -1 \\ 4 \end{pmatrix} = 2x + x(-1) + 3(4) = 2x - x + 12 = x + 12 = 0

📌 x + 12 = 0 \Rightarrow x = \boxed{-12}

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