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JEE Main20236 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let the image of the point P ( 1 ,   2 ,   3 ) in the plane 2 x – y + z = 9 be Q . If the coordinates of the point R are ( 6 ,   10 ,   7 ) , then the square of the area of the triangle P Q R is _ _ _ _ _ _ _ .

Correct answer

594

Step-by-step solution

Given, The image of the point P ( 1 ,   2 ,   3 ) in the plane 2 x – y + z = 9 be Q , The coordinates of the point R are ( 6 ,   10 ,   7 ) , Now plotting the diagram we get, R lies on plane as 6 , 10 , 7 satisfy the plane equation 2 x – y + z = 9 Now length of P R = 5 2 + 8 2 + 4 2 = 105 Now finding the angle between P R   &   P M (which is normal vector to plane) we get, cos θ = P R → · P M → P R → · P M → ⇒ cos θ = (

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