3x + 4(-6) = 0
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- Two vectors \(egin{pmatrix} a \ b \end{pmatrix}\) and \(egin{pmatrix} c \ d \end{pmatrix}\) are orthogonal if their dot product is zero: \(a \cdot c + b \cdot d = 0\).
- Given vectors:
- egin{pmatrix} 3 \ 4 \end{pmatrix} \quad ext{and} \quad egin{pmatrix} x \ -6 \end{pmatrix}
- 3x - 24 = 0
- 3x = 24 \quad \Rightarrow \quad x = 8
- Thus, the value of \(x\) that makes the vectors orthogonal is \(oxed{8}\).
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