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JEE Main202229 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

If the mirror image of the point 2 , 4 , 7 in the plane 3 x - y + 4 z = 2 is a , b , c , the 2 a + b + 2 c is equal to

Options

  1. A54
  2. B- 6
  3. C50
  4. D- 42

Correct answer

B. - 6

Step-by-step solution

Given, equation of 3 x - y + 4 z = 2 and point P 2 , 4 , 7 Now using the formula of image x - x 1 a = y - y 1 b = z - z 1 c = - 2 × a x 1 + b y 1 + c z 1 + d a 2 + b 2 + c 2 We get, x - 2 3 = y - 4 - 1 = z - 7 4 = - 2 6 - 4 + 28 - 2 26 ⇒   x - 2 3 = y - 4 - 1 = z - 7 4 = - 28 13 ⇒     x = - 58 13 , y = 80 13 , z = - 21 13 Hence, 2 a + b + 2 c = - 116 13 + 80 13 - 42 13 = - 6

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