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  • If <img alt="\left| {{{\vec{A}}}_{1}} \right|=3,\left| {{{\vec{A}}}_{2}} \right|=5\And \left| {{{\vec{A}}}_{1}}+{{{\vec{A}}}_{2}} \right|=5." src="https://entrancecorner.oncodecogs.com/gi

If \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 (2{{\vec{A}}_{1}}+3{{\vec{A}}_{2}}).(3{{\vec{A}}_{1}}-2{{\vec{A}}_{2}}) is

Option: 1

-106.5


Option: 2

-99.5
 


Option: 3

-118.5

 


Option: 4

-112.5


Answers (1)

best_answer

\begin{aligned} & \left(| {A_1}+ {A}_2|\right)^2=A_1^2+A_2^2+2 A_1. A_2=25 \\ & {A_1 \cdot A_2}=\frac{1}{2}(25-9-25)=-\frac{9}{2} \\ & \end{aligned}

So,
(2{{{\vec{A}}}_{1}}+3{{{\vec{A}}}_{2}}).(3{{{\vec{A}}}_{1}}-2{{{\vec{A}}}_{2}})=6\vec{A}_{1}^{2}-4{{{\vec{A}}}_{1}}{{{\vec{A}}}_{2}}+9{{{\vec{A}}}_{2}}{{{\vec{A}}}_{1}}-6A_{2}^{2} \\ (2{{{\vec{A}}}_{1}}+3{{{\vec{A}}}_{2}}).(3{{{\vec{A}}}_{1}}-2{{{\vec{A}}}_{2}})=6(9)+5(\frac{-9}{2})-6(25) \\ (2{{{\vec{A}}}_{1}}+3{{{\vec{A}}}_{2}}).(3{{{\vec{A}}}_{1}}-2{{{\vec{A}}}_{2}})=-118.5 \\

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Pankaj

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