InterviewSolution
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InterviewSolution
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Let ` vec a , vec b, vec c`be three non-zero vectors such that any two ofthem are non-collinear. If ` vec a+2 vec b`is collinear with ` vec ca n d vec b+3 vec c`is collinear with ` vec a`then prove that ` vec a+2 vec b+6 vec c= vec0`A. `lambda vec(a)`B. `lambda vec(b)`C. `lambda vec(c)`D. `vec(0)` |
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Answer» Correct Answer - D It is given that `vec(a) + 2 vec(b) ` is collinear with ` vec(c ) and vec(b) + 3 vec( c) ` is collinear with `vec(a).` ` therefore vec(a) + 2 vec(b) = x vec(c ), and vec(b) + 3 vec( c) =y vec(a) " for some " x, y in R` `therefore vec(a) + 2 vec(b) +6 vec(c)=(x+6) vec(c ) ` Also, `vec(a)+2 vec(b)+6 vec(c ) = (1+2y) vec(a)` `therefore (x+6) vec(c) = (1+2y) vec(a) ` `rArr x+6=0 and 1+2y =0 " " [ because vec(a), vec(c ) " are non- collinear ]` `rArr x= -6 and y= -1//2` `rArr vec(a) + 2 vec(b) + 6 vec(c ) = vec(0)` |
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