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

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

Column $-I$	Column $-II$
$(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$	$(i)$ $\theta = \,{0^o}$
$(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$	$(ii)$ $\theta = \,{90^o}$
$(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$	$(iii)$ $\theta = \,{180^o}$
$(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$	$(iv)$ $\theta = \,{60^o}$

Column $-I$	Column $-II$
$(a)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,0$	$(i)$ $\theta = \,{30^o}$
$(b)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,8$	$(ii)$ $\theta = \,{45^o}$
$(c)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,4$	$(iii)$ $\theta = \,{90^o}$
$(d)$ $\left\| {\vec A \, \times \,\,\vec B } \right\|\, = \,\,4\sqrt 2$	$(iv)$ $\theta = \,{0^o}$

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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