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3-1.Vectors
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સદિશ $\overrightarrow {\rm A} = 2\hat i + 3\hat j - \hat k$નો સદિશ $\overrightarrow B = - \hat i + 3\hat j + 4\hat k$ ની દિશામાંનો પ્રક્ષેપ મેળવો.
A
$\frac{3}{{\sqrt {13} }}$
B
$\frac{3}{{\sqrt {26} }}$
C
$\sqrt {\frac{3}{{26}}} $
D
$\sqrt {\frac{3}{{13}}} $
Solution
(b) $|\overrightarrow {\rm A} |\, = \,\sqrt {{2^2} + {3^2} + {{( – 1)}^2}} $$ = \sqrt {4 + 9 + 1} $ $ = \sqrt {14} $
$|\overrightarrow B |\, = \,\sqrt {{{( – 1)}^2} + {3^2} + {4^2}} $ $ = \sqrt {1 + 9 + 16} $ $ = \sqrt {26} $
$\overrightarrow A \,.\,\overrightarrow B = \,2\,( – 1) + 3 \times 3 + ( – 1)\,(4) = 3$
The projection of $\overrightarrow A \,\,{\rm{on}}\,\overrightarrow B $ $ = \frac{{\overrightarrow A \,.\,\overrightarrow B }}{{|\overrightarrow B |}}$ $ = \frac{3}{{\sqrt {26} }}$
Standard 11
Physics
