InterviewSolution
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InterviewSolution
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` vec a , vec b , vec c`are three coplanar unit vectors such that ` vec a+ vec b+ vec c=0.`If three vectors ` vec p , vec q ,a n d vec r`are parallel to ` vec a , vec b ,a n d vec c ,`respectively, and have integral butdifferent magnitudes, then among the following options, `| vec p+ vec q+ vec r|`can take a value equal toa. `1`b. `0`c. `sqrt(3)`d. `2`A. 1B. 0C. `sqrt(3)`D. 2 |
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Answer» Correct Answer - C::D Let a,b and c lie in the XY-plane Let `a=hati,b=-(1)/(2)hati+(sqrt(3))/(2)hatj and c=-(1)/(2)hati-(sqrt(3))/(2)hatj` Therefore, `|p+q+r|=|lamda a+mub+vc|` `=|lamdahati+mu(-(1)/(2)hati+(sqrt(3))/(2)hatj)+v(-(1)/(2)hati-(sqrt(3))/(2)hatj)|` `|(lamda+(mu)/(2)-(v)/(2))hati+(sqrt(3))/(2)(mu-v)hatj|` `=sqrt((lamda-(mu)/(2)-(v)/(2))^(2)+(3)/(4)(mu-v)^(2))` `=sqrt(lamda^(2)+mu^(2)+v^(2)-lamdamu-lamdav-muv)` `=(1)/(sqrt(2))sqrt((lamda-mu)^(2)+(mu-v)^(2)+(v-lamda)^(2))` `=(1)/(sqrt(2))sqrt(1+1+4)=sqrt(3)`. |
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