જો , a = , , , i , , + ;2 j , , , - , ,2 k , ,, , , b , = , ,2 i … - Vidyadip

MCQ

જો $\,\vec a = \,\,\,\hat i\,\, + \;2\hat j\,\,\, - \,\,2\hat k\,\,,\,\,\vec b \, = \,\,2\hat i\,\, - \;\hat j\,\,\, + \,\hat k$ અને $\vec c \,\, = \,\,\hat i\,\, + \;3\hat j\,\,\, - \,\hat k\,\,$ અને $\,\,\,\vec a \,\, \times \,\,\left( {\,\vec b \, \times \,\vec c } \right)\,\, = \,\,....$

A
$\,20\hat i\,\, - \;3\hat j\,\,\, + \,\,7\hat k\,\,$
B
$\,20\hat i\,\, + \;3\hat j\,\,\, + \,\,7\hat k\,\,$
C
$\,20\hat i\,\, + \;3\hat j\,\,\, - \,\,7\hat k\,\,$
D
આપેલ પૈકી એકપણ નહીં.

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Answer

$\vec a \,\, \times \,\,\left( {\,\vec b \, \times \,\vec c } \right)\, = \,\left( {\vec a .\,\,\vec c } \right)\,\vec b \,\, - \,\,\left( {\vec a \,.\,\vec b } \right)\,\,\vec c $

$\vec a .\,\,\vec c \,\, = \,\,\left( 1 \right)\,\,\left( 1 \right)\,\, + \;\,\left( 2 \right)\,\,\left( 3 \right)\,\, + \;\,\left( { - 2} \right)\,\,\left( { - 1} \right)\,\, = \,\,9$

$\vec a \,.\,\vec b \,\, = \,\,\left( 1 \right)\,\,\left( 2 \right)\,\, + \;\,\left( 2 \right)\,\,\left( { - 1} \right)\,\, + \;\,\left( { - 2} \right)\,\,\left( 1 \right)\,\, = \,\, - 2$

$\therefore \,\,\vec a \, \times \,\,\left( {\vec b \,\, \times \,\,\vec c \,} \right)\,\,$

$ = \,\,\left( 9 \right)\,\,\left( {2\hat i\,\, - \,\hat j\,\, + \;\,\hat k} \right)\,\, - \,\,\left( { - 2} \right)\,\,\left( {\hat i\,\, + 3\hat j\,\, - \;\,\hat k} \right)$

$ = \,\,18\hat i\,\, - \,9\hat j\,\, + \;\,9\hat k\,\, - \,\,\left( { - 2\hat i\,\, - \,6\hat j\,\, + \;\,2\hat k} \right)\,\, $

$= \,\,20\hat i\,\, - \,3\hat j\,\, + \;\,7\hat k$

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