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3-1.Vectors
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બે સદિશો $ \overrightarrow A $ અને $ \overrightarrow B $ વચ્ચેનો ખૂણો $ \theta $ છે. ત્રિ-ગુણાંક $ \overrightarrow A \cdot (\overrightarrow B \times \overrightarrow A)$ નું મૂલ્ય કેટલું થાય?
A
$ {A^2}B $
B
શૂન્ય
C
$ {A^2}B\sin \theta $
D
$ {A^2}B\cos \theta $
(AIPMT-2005) (AIPMT-1991)
Solution
(b) Let $\overrightarrow A \,.(\overrightarrow B \, \times \overrightarrow A ) = \overrightarrow A \,.\,\overrightarrow C \,$
Here $\overrightarrow C = \overrightarrow B \times \overrightarrow A $ Which is perpendicular to both vector
$\overrightarrow A $ and $\overrightarrow B $
$\therefore\,\overrightarrow A \,.\overrightarrow {\,C} = 0$
Standard 11
Physics
