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STD 12 - 10. vector algebra — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. vector algebra4 Marks
Question
If $a,b,c$  are vectors such that  $[abc\,]=4$   , then $[a\times b\,\,b\times c\,\,c\times a]$  =  
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Answer

a
(a) $[a \times b\,\,b\, \times c\,\,c \times a] = (a \times b)\,.\,[(b \times c) \times (c \times a)]$

$ = (a \times b)\,.\,(\,[b\,c\,a]\,c - [b\,c\,c]\,a)$$ = (a \times b)\,.\,(\,[b\,c\,a]\,c - 0)$

$ = [b\,c\,a]\,[a\,b\,c] = [a\,b\,c]\,[a\,b\,c] = 4.4 = 16.$

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