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JEE Main20244 Apr 2024Morning ShiftMathematicsVector AlgebraActual

Let ABC be a triangle of area 15 2 and the vectors AB = i +2 j -7 k , BC = a i + b j + ck and AC =6 i + d j -2 k , ~d >0 . Then the square of the length of the largest side of the triangle ABC is _______

Correct answer

0

Step-by-step solution

aligned & Area = 1 2 | array ccc i & j & k 1 & 2 & -7 6 & d & -2 array |=15 2 & (-4+7 d) i - j (-2+42)+ k (d-12) & (7 d-4)^2+(40)^2+(d-12)^2=1800 & 50 d^2-80 d-40=0 & 5 d^2-8 d-4=0 & 5 d^2-10 d-2 d-4 & 5 d(d-2)+2(d-2)=0 & d=2 or d=- 2 5 & d>0, d=2 & (a+1) i +(b+2) j +(c-7) k =6 i +2 j -2 k & a+1=6 & b+2=2, c-7=-2 & a=5 b=0 c=5 & |A B|= 1+4+49 = 54 & |B C|= 25+25 = 50 & |A C|= 86+4+4 = 44 aligned Ans. 54

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