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3-1.Vectors
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જો $\,{\rm{|}}\mathop {\rm{A}}\limits^ \to \,\, + \;\,\mathop B\limits^ \to \,|\,\, = \,\,\,{\rm{|}}\mathop {\rm{A}}\limits^ \to \,\, - \;\,\mathop B\limits^ \to \,|\,$ હોય $\vec A $ અને $\vec B $ વચ્ચેનો ખૂણો ........ $^o$
A
$35$
B
$45$
C
$60$
D
$90$
Solution
$\begin{array}{l}
\,{\rm{|}}\mathop {\rm{A}}\limits^ \to + \;\mathop B\limits^ \to \,|= {\rm{|}}\mathop {\rm{A}}\limits^ \to \,\, – \;\,\mathop B\limits^ \to \,|\,\, \\ \Rightarrow \,\,\sqrt {{A^2} + \;{B^2}+ \;2AB \cos \theta } = \sqrt {{A^2} + \;\,{B^2}\, – 2AB \cos \,\theta } \\
\Rightarrow \,\,{A^2} + \;{B^2}+ \;\;2AB\,\,\cos \,\,\theta \,\, = \,\,{A^2} + {B^2} – 2AB\cos \theta \\ \Rightarrow cos \theta = 0\, \\ \therefore \,\theta = 90^\circ
\end{array}$
Standard 11
Physics
