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  • Let a,b and c be distinct non-negative numbers . if vectors ai+aj+ck , i+j and ci+cj+ck are copl- nar then c is

Let a,b and c be distinct non-negative numbers . if vectors ai+aj+ck , i+j and ci+cj+ck are copl- nar then c is

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Solution:   a,b  and  c  are distnct negative numbers and vectors 

          ai+aj+ck ,i+k   and  ci+cj+bk  are coplanar 

                                  \ \ Rightarrow hspace1cmeginvmatrix a &a &c \ 1 & 0 & 1\ c& c& b endvmatrix=0\ \ Rightarrow hspace1cm ac+c^2-ab-ac=0Rightarrow c^2=ab

    Hence     a,b,c    are in GP  . So  c  is the GM of   a   and   b.

Posted by

Deependra Verma

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