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4. Sean los vectores: \( \mathbf{A}=2,0 \boldsymbol{i}-3,0 \mathrm{j} \) y \( \mathrm{B}=3,0 \mathrm{f}-2,0 \mathrm{f} \). Para esta situación el módulo del vector resultante de la operación matemática: \( 2,0 \cdot \mathbf{A}-3,0 \cdot \mathrm{~B} \), vendrá dado por:

Ask by Gibson Elliott. in Argentina
Mar 15,2025

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El módulo del vector resultante es 5.0.

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Primero, realizamos las operaciones con los vectores. Multiplicamos \( \mathbf{A} \) y \( \mathbf{B} \) por sus respectivos coeficientes: \( 2,0 \cdot \mathbf{A} = 2,0 \cdot (2,0 \boldsymbol{i}-3,0 \mathrm{j}) = 4,0 \boldsymbol{i} - 6,0 \mathrm{j} \) \( 3,0 \cdot \mathbf{B} = 3,0 \cdot (3,0 \boldsymbol{i}-2,0 \mathrm{j}) = 9,0 \boldsymbol{i} - 6,0 \mathrm{j} \) Luego, restamos estos resultados: \( (4,0 \boldsymbol{i} - 6,0 \mathrm{j}) - (9,0 \boldsymbol{i} - 6,0 \mathrm{j}) = -5,0 \boldsymbol{i} + 0 \mathrm{j} \) El módulo del vector resultante, \( |\mathbf{R}| \), es simplemente \( 5,0 \). El resultado correcto para el módulo del vector resultante de la operación dada es \( 5,0 \).

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