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MHT CET202312 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If the area of the triangle with vertices (1,2,0) , (1,0,2) and (0, x, 1) is 6 square units, then the value of x is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

aligned & Let A (1,2,0), B (1,0,2) and C (0, x, 1) & AB =-2 j +2 k and AC =- i +(x-2) j + k & Area of ABC = 1 2 | AB AC |= 6 & | AB AC |= | array ccc i & j & k 0 & -2 & 2 -1 & x-2 & 1 array | & = i [-2-2(x-2)]- j (0+2)+ k (0-2) & =(2-2 x) i -2 j -2 k & 1 2 | AB AC |= 6 & 1 2 (2-2 x)^2+4+4 = [6] 6 & (2-2 x)^2=16 & 4-8 x+4 x^2=16 & x^2-2 x+3=0 & (x-3)(x+1)=0 & x=3 or -1 & aligned

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