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JEE Main20249 Apr 2024Morning ShiftMathematicsVector AlgebraActual

Let three vectors a = i +4 j +2 k , b =5 i +3 j +4 k , c =x i +y j +z k form a triangle such that c = a - b and the area of the triangle is 5 6 . If is a positive real number, then | c |^2 is equal to:

Options

  1. A16
  2. B14
  3. C12
  4. D10

Correct answer

B. 14

Step-by-step solution

aligned & c = a - b & ( x , y , z )=( -5,1,-2) & x = -5, y =1, z =-2.....(1) aligned Area of =5 6 (given) aligned & 1 2 | a c |=5 6 & | array ccc i & j & k & 4 & 2 x & 1 & -2 array |=10 6 aligned aligned & |-10 i - j (-2 -2 x )+ k ( -4 x )|=10 6 & (2 +2 -10)^2+( -4 +20)^2=500 & (4 -10)^2+(20-3 )^2=500 & 25 ^2-80 -120 =0 & (25 -200)=0 & =8 (given is +ve number) & x = -5=3 & | c |^2= x ^2+ y ^2+ z ^2 & =9+1+4 & =14 aligned

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