Question

calcule o modelo do vetor resultante ​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Regra~do~paralelogramo:}\\\sf \overrightarrow{\sf F_R}^2=\overrightarrow{\sf a}^2+\overrightarrow{\sf b^2}+2\cdot a\cdot b\cdot cos(\theta)\end{array}}$$\Large\boxed{\begin{array}{l}\rm Calcule~o~m\acute odulo~do~vetor~resultante:\\\tt a)~\rm Dados~~\begin{cases}\sf a=6~cm\\\sf b=5\sqrt{2}~cm\\\sf cos(45^\circ)=\dfrac{\sqrt{2}}{2}\end{cases}\\\\\tt b)~\rm Dados~~\begin{cases}\sf a=5~m\\\sf b=8~m\\\sf cos(120^\circ)=-0,5\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao\!:}\\\tt a)~\sf\overrightarrow{\sf F_R}^2=6^2+(5\sqrt{2})^2+\diagup\!\!\!2\cdot6\cdot5\sqrt{2}\cdot\dfrac{\sqrt{2}}{\diagup\!\!\!2}\\\sf\overrightarrow{\sf F_R}^2=36+50+60\\\sf \overrightarrow{\sf F_R}^2=146\\\sf\overrightarrow{\sf F_R}=\sqrt{146}~cm\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)~\sf\overrightarrow{\sf F_R}^2=5^2+8^2+\diagup\!\!\!2\cdot5\cdot8\cdot-\dfrac{1}{\diagup\!\!\!2}\\\sf \overrightarrow{\sf F_R}^2=25+64-40\\\sf\overrightarrow{\sf F_R}^2=49\\\sf \overrightarrow{\sf F_R}=\sqrt{49}\\\sf\overrightarrow{\sf F_R}=7~m\end{array}}$