A ray of light through the point A 1,2 , 3 strikes the plane x + y + z = 12 at a point B and on reflection passes through the point C 3,5 , 9 . If the equation of a plane containing the incident ray and the reflected ray is P = 0 and the distance of P = 0 from 0,0 , 0 is λ units, then the value of 13 λ 2 is equal to

Question

A ray of light through the point A 1,2 , 3 strikes the plane x + y + z = 12 at a point B and on reflection passes through the point C 3,5 , 9 . If the equation of a plane containing the incident ray and the reflected ray is P = 0 and the distance of P = 0 from 0,0 , 0 is λ units, then the value of 13 λ 2 is equal to, 1, 2, 4, 6

MARKS App · Accepted Answer

A plane which contains the incident ray and the reflected ray must contain the points A , B , C and should be perpendicular to the given plane. So, equation of the plane is x - 1 y - 2 z - 3 1 1 1 2 3 6 = 0 ⇒ x - 1 3 - y - 2 4 + z - 3 3 - 2 = 0 ⇒ 3 x - 3 - 4 y + 8 + z - 3 = 0 ⇒ 3 x - 4 y + z + 2 = 0 Hence, the distance of the plane from 0,0 , 0 is 0 - 0 + 0 + 2 9 + 16 + 1 = 2 26 units

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