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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
Let  $a, b,c $ be three vectors from ,  $a\times (b\times c)=(a\times b)\times c$ if 
  • ✓
    $b\times (a\times c)=0$
  • B
    $a(b\times c)=0$
  • C
    $c \times a = a \times b$
  • D
    $c\times b=b\times a$
✓

Answer

Correct option: A.
$b\times (a\times c)=0$
a
(a) $\because $  We have $a \times (b \times c) = (a \times b) \times c$

 $ \Rightarrow \,\,(a\,.\,c)\,b - (a\,.\,b)\,c = (a\,.\,c)\,b - (b\,.\,c)\,a$
 

$ \Rightarrow - \,(a\,.\,b)\,c = - \,(b\,.\,c)\,a$$ \Rightarrow \,\,(b\,.\,c)\,a - (b\,.\,a)\,c = 0$

$ \Rightarrow \,\,b \times (a \times c) = 0.$

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