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3-1.Vectors
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જો સદિશ $ \overrightarrow A = 2\hat i + 4\hat j - 5\hat k $ ,હોય તો સદીશનો દિશાકીય cosine કેટલો થાય?
A$ \frac{2}{{\sqrt {45} }},\frac{4}{{\sqrt {45} }}\,$અને$\,\frac{{ - \,{\rm{5}}}}{{\sqrt {{\rm{45}}} }} $
B$ \frac{1}{{\sqrt {45} }},\frac{2}{{\sqrt {45} }}\,$અને$\,\frac{{\rm{3}}}{{\sqrt {{\rm{45}}} }} $
C$ \frac{4}{{\sqrt {45} }},\,0\,$અને$\,\frac{{\rm{4}}}{{\sqrt {45} }} $
D$ \frac{3}{{\sqrt {45} }},\frac{2}{{\sqrt {45} }}\,$અને$\,\frac{{\rm{5}}}{{\sqrt {{\rm{45}}} }} $
Solution
(a) $\vec A = 2\hat i + 4\hat j – 5\hat k$
$|\overrightarrow A |\, = \sqrt {{{(2)}^2} + {{(4)}^2} + {{( – 5)}^2}} \, = \,\sqrt {45} $
$\cos \alpha = \frac{2}{{\sqrt {45} }},\,\,\,\,\,\cos \beta = \frac{4}{{\sqrt {45} }},\,\,\,\,\cos \gamma = \frac{{ – 5}}{{\sqrt {45} }}$
$|\overrightarrow A |\, = \sqrt {{{(2)}^2} + {{(4)}^2} + {{( – 5)}^2}} \, = \,\sqrt {45} $
$\cos \alpha = \frac{2}{{\sqrt {45} }},\,\,\,\,\,\cos \beta = \frac{4}{{\sqrt {45} }},\,\,\,\,\cos \gamma = \frac{{ – 5}}{{\sqrt {45} }}$
Standard 11
Physics
