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`bara` & `barb` be two vectors such that `|a|=1,|b|=4`& `bara.barb=2`. If `barc=(2baraxxbarb)-3barb`, then which of the following is/are correct?A. `barb.barc=48`B. `barb.barc=-48`C. Angle between `barb` & `barc` is`(5pi)/6`D. Angle between `barb` & `barc` is `(pi)/6`. |
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Answer» Correct Answer - B::C `|bara|=1, |barb|=4, bara.barb=2` & `barc+3barb=2baraxxbarb` `Q bara.barb=2` `impliescostheta=2/(|bara||barb|)=1/2 impliestheta =(pi)/3` Agai `|barc+3barb|^(2)=|2baraxxbarb|^(2)` `implies |barc|^(2)+9|barb|^(2)+2barc.3barb=4|bara|^(2)|barb|^(2)sin^(2)theta` `implies|barc|^(2)+144+6barb.barc=48` Also, `barc=2baraxxbarb-3barb` `impliesbarc.barc=barb(2baraxxbarb)-3|barb|^(2)` `impliesbarc.barc=0-3xx16=-48` `:.|barc|^(2)+96-6xx48=0` `=|barc|^(2)=192` `implies|barc|=8sqrt(3)` `barb.barc=|barb||barc|=cos alphaimplies -48=4xx8sqrt(3) cos alpha` `impliescos alpha=-6/(4sqrt(3))=-(sqrt(3))/2` `impliesalpha=(5pi)/6` |
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