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If veca, vecb, vecc non-zero vectors such that veca is perpendicular to vecb and vecc and |veca|=1, |vecb|=2, |vecc|=1, vecb.vecc=1. There is a non-zero vector coplanar with veca+vecb and 2vecb-vecc and vecd.veca=1, then the minimum value of |vecd| is |
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Answer» `2/SQRT(13)` but `vecd.veca=1 rArr 1=x(1+0)+0 rArr x=1` `rArr vecd=veca +vecb+y(2vecb-vecc)` `rArr |vecd|^(2)=|veca|^(2)+|b|^(2)=2veca.vecb+y^(2)(2vecb-vecc)^(2)+2y(veca+vecb).(2vecb-vecc)` `rArr =1+4+y^(2)(16+1-4)+2y(8-1)` `=13y^(2)+14y+5` `therefore |vecd|_("MIN" ) = sqrt((4.13.5-14.14)/(4.13))=4/sqrt(13)` |
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