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If the points A 3 - x , 3 , 3 , B 3 , 3 - y , 3 , C 3 , 3 , 3 - z and D 2 , 2 , 2 are coplanar, then 1 x + 1 y + 1 z is equal to

Options

  1. A- 1
  2. B1
  3. C3
  4. D5

Correct answer

B. 1

Step-by-step solution

D A → = < 1 - x , 1 , 1 > D B → = < 1 , 1 - y , 1 > D C → = < 1 , 1 , 1 - z > ∴ A , B , C , D are coplanar ⇒ D A → D B → D C → = 0 1 - x 1 1 1 1 - y 1 1 1 1 - z = 0 ⇒ 1 - x 1 - y 1 - z - 1 - 1 - z - 1 + 1 1 - 1 - y = 0 ⇒ 1 - x - y - z + y z + z + y = 0 ⇒ - y - z + y z + x y + x z - x y z + z + y = 0 ⇒ x y + y z + z x = x y z ⇒ 1 x + 1 y + 1 z = 1

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