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3-1.Vectors
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સદિશ $\mathop A\limits^ \to \,\, = \,\,\hat i\,\, + \;\,\hat j\,\, + \;\,\hat k$ નો અનુક્રમે $X$, $Y$ અને $Z$ અક્ષ સાથેના ખૂણાનું cosine મૂલ્ય ......
A$\frac{1}{{\sqrt 3 }},\frac{1}{{\sqrt 3 }},\frac{1}{{\sqrt 3 }}$
B$\frac{1}{{\sqrt 3 }},\frac{2}{{\sqrt 3 }},\frac{3}{{\sqrt 3 }}$
C$\frac{1}{{\sqrt 3 }},\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 2 }}$
D$\frac{1}{{\sqrt 2 }},\frac{1}{{\sqrt 3 }},\frac{2}{{\sqrt 3 }}$
Solution
$A_x = A_y = A_z = 1 $
$\,{\rm{A}}\,\, = \,\,\sqrt {{{\rm{A}}_{\rm{x}}}^2\,\, + \;\,{A_y}^2\,\, + \;\;{A_z}^2} \,\, = \,\,\sqrt {1\,\, + \,\,1\,\, + \;\;1} \,\, = \,\,\,\sqrt {\rm{3}} $
${\rm{cos}}\,\,\alpha \,\, = \,\,\frac{{{{\rm{A}}_{\rm{x}}}}}{{\rm{A}}}\,\, = \,\,\frac{1}{{\sqrt 3 }}$
$\cos \,\,\beta \,\, = \,\,\frac{{{A_y}}}{A}\,\, = \,\,\frac{1}{{\sqrt 3 }}$
$\cos \,\gamma \,\, = \,\,\frac{{{A_z}}}{A}\,\, = \,\,\frac{1}{{\sqrt 3 }}$
$\,{\rm{A}}\,\, = \,\,\sqrt {{{\rm{A}}_{\rm{x}}}^2\,\, + \;\,{A_y}^2\,\, + \;\;{A_z}^2} \,\, = \,\,\sqrt {1\,\, + \,\,1\,\, + \;\;1} \,\, = \,\,\,\sqrt {\rm{3}} $
${\rm{cos}}\,\,\alpha \,\, = \,\,\frac{{{{\rm{A}}_{\rm{x}}}}}{{\rm{A}}}\,\, = \,\,\frac{1}{{\sqrt 3 }}$
$\cos \,\,\beta \,\, = \,\,\frac{{{A_y}}}{A}\,\, = \,\,\frac{1}{{\sqrt 3 }}$
$\cos \,\gamma \,\, = \,\,\frac{{{A_z}}}{A}\,\, = \,\,\frac{1}{{\sqrt 3 }}$
Standard 11
Physics
