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JEE Main202229 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

Let Q be the foot of perpendicular drawn from the point P 1 , 2 , 3 to the plane x + 2 y + z = 14 . If R is a point on the plane such that ∠ P R Q = 60 ° , then the area of ∆ P Q R is equal to

Options

  1. A3 2
  2. B3
  3. C2 3
  4. D3

Correct answer

B. 3

Step-by-step solution

Given Q be the foot of perpendicular drawn from the point P 1 , 2 , 3 to the plane x + 2 y + z = 14 . If R is a point on the plane such that ∠ P R Q = 60 ° , then the area of ∆ P Q R is equal to Now plotting the diagram of given value we get, Now given plane x + 2 y + z = 14 Length of perpendicular from P   to   Q will be P Q = 1 + 4 + 3 - 14 6 = 6 Now in △ P Q R Q R = P Q cot 60 ° = 2 So, Area of ∆ P Q R = 1 2 P Q Q R = 1 2 × 6 × 2 = 3

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