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JEE Main20253 Apr 2025Morning ShiftMathematicsVector AlgebraActual

Let a = i + j + k , b =3 i +2 j - k , c = j + k and d be a unit vector such that a d = b d and c d =1 , If c is perpendicular to a , then |3 d + c |^2 is equal to _______ .

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0

Step-by-step solution

aligned & a d - b d =0 & ( a - b ) d =0 & ~d = t ( a - b ) & d = t (-2 i - j +2 k ) & | d |=1 & | t |= 1 3 aligned aligned & c a =0 & + =0 & =- & c = ( j - k ),| c |^2=2 ^2 & c d =1 & t (-2,-1,2) (0,1,-1)=1 & t = -1 3 ^2=1 aligned aligned & |3 ~d + c |^2=9 ^2| ~d |^2+ ^2| c |^2+6 ( ~d c ) & =3 ^2+2 ^4 & =5 aligned

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