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3-1.Vectors
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$\vec A$ અને $\vec B $ નો પરિણામી સદીશ $\vec R_1$ છે . વિરુદ્ધ સદીશ $\vec B $ પર પરિણામી સદીશ $\vec R_2 $ બને તો ${\rm{R}}_{\rm{1}}^{\rm{2}}\,\, + \,\,{\rm{R}}_{\rm{2}}^{\rm{2}}$ નું મૂલ્ય શું હશે ?
A
$A^2 + B^2$
B
$A^2- B^2$
C
$2(A^2 + B^2)$
D
$2(A^2- B^2)$
Solution
$\,\mathop A\limits^ \to \,\, + \,\,\mathop B\limits^ \to \,\, = \,\,\mathop {{R_1}}\limits^ \to $
અને $\,\mathop A\limits^ \to \,\, – \,\,\mathop B\limits^ \to \,\, = \,\,\mathop {{R_2}}\limits^ \to $
$ \Rightarrow \,\,R_1^2\,\, + \;\,R_2^2 = \,\,\left( {{A^2}\,\, + \;\,{B^2}\,\, + \;2AB\cos \theta } \right)\,\, + \;\,\,\left( {{A^2}\,\, + \;\,{B^2}\,\, – \,\,2AB\,\cos \theta } \right) = \,\,2\left( {{A^2}\,\, + \;\,{B^2}} \right)\;$
Standard 11
Physics
