Let left| {{{vec A}_1}} right| = 3,,left | vedclass

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Question

$\begin{array}{l}
\left| {{{\vec A}_1}} ight| = 3,\left| {{{\vec A}_2}} ight| = 5,\,and\,\left| {{{\vec A}_1} + {{\vec A}_2}} ight| = 5.\
\le

Vedclass · Accepted Answer

$-118.5$

Vedclass · Answer

$\begin{array}{l}
\left| {{{\vec A}_1}} ight| = 3,\left| {{{\vec A}_2}} ight| = 5,\,and\,\left| {{{\vec A}_1} + {{\vec A}_2}} ight| = 5.\
\left| {{{\vec A}_1} + {{\vec A}_2}} ight| = {\left| {{{\vec A}_1}} ight|^2} + {\left| {{{\vec A}_2}} ight|^2} + 2\left| {{{\vec A}_1}} ight|\left| {{{\vec A}_2}} ight|\,\cos \,	heta \
\cos \,	heta \, =  - \frac{3}{{10}}\
\left( {2{{\vec A}_1} + 3{{\vec A}_2}} ight).\left( {3{{\vec A}_1} - 2{{\vec A}_2}} ight)\
 = 6{\left| {{{\vec A}_1}} ight|^2} + 9{{\vec A}_1}.{{\vec A}_2} - 4{{\vec A}_1}.{{\vec A}_2} - 6{\left| {{{\vec A}_2}} ight|^2}\
 =  - 118.5
\end{array}$

Let $\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5$, and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5$. The value of $\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)$ is

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