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3-1.Vectors
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સદિશ $\mathop {\rm{P}}\limits^ \to $ $ \alpha, \beta $ અને $ \gamma $ સાથે અનુક્રમે $ X, Y$ અને $Z$ ખૂણા બનાવે છે.તો $ {sin^2}\alpha + {sin^2} \beta + {sin^2} \gamma $ =
A
$0$
B
$1$
C
$2$
D
$3$
Solution
${\cos ^2}\alpha \,\, + \;\,{\cos ^2}\beta \,\, + \;\,{\cos ^2}\gamma \, = \,\,1$
$\left( {1\, – \,\,{{\sin }^2}\alpha } \right)\,\, + \;\;\left( {1\,\, – \,\,{{\sin }^2}\beta } \right)\,\, + \;\,\left( {1\,\, – \,\,{{\sin }^2}\gamma } \right)\,\, = \,\,1$
${\sin ^2}\alpha \,\, + \;\;{\sin ^2}\beta \,\, + \;\,{\sin ^2}\gamma \,\, = \,\,3\,\, – \,1\,\, = \,\,2\,$
Standard 11
Physics
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