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3-1.Vectors
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सदिशों $\mathop A\limits^ \to = 4\hat i + 3\hat j + 6\hat k$ तथा $\mathop B\limits^ \to = - \hat i + 3\hat j - 8\hat k$ के परिणामी सदिश के समांतर इकाई सदिश है
A$\frac{1}{7}(3\hat i + 6\hat j - 2\hat k)$
B$\frac{1}{7}(3\hat i + 6\hat j + 2\hat k)$
C$\frac{1}{{49}}(3\hat i + 6\hat j - 2\hat k)$
D$\frac{1}{{49}}(3\hat i - 6\hat j + 2\hat k)$
Solution
(a) सदिश $\mathop A\limits^ \to $ तथा $\mathop B\limits^ \to $का परिणामी
$\mathop R\limits^ \to = \mathop A\limits^ \to + \mathop B\limits^ \to = 4\hat i + 3\hat j + 6\hat k – \hat i + 3\hat j – 8\hat k$$ = 3\hat i + 6\hat j – 2\hat k$
$\hat R = \frac{{\mathop R\limits^ \to }}{{|\mathop R\limits^ \to |}} = \frac{{3\hat i + 6\hat j – 2\hat k}}{{\sqrt {{3^2} + {6^2} + {{( – 2)}^2}} }} = \frac{{3\hat i + 6\hat j – 2\hat k}}{7}$
$\mathop R\limits^ \to = \mathop A\limits^ \to + \mathop B\limits^ \to = 4\hat i + 3\hat j + 6\hat k – \hat i + 3\hat j – 8\hat k$$ = 3\hat i + 6\hat j – 2\hat k$
$\hat R = \frac{{\mathop R\limits^ \to }}{{|\mathop R\limits^ \to |}} = \frac{{3\hat i + 6\hat j – 2\hat k}}{{\sqrt {{3^2} + {6^2} + {{( – 2)}^2}} }} = \frac{{3\hat i + 6\hat j – 2\hat k}}{7}$
Standard 11
Physics
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