If the product of distances of the point (1, 1, 1) from the origin and the plane x – y + z + λ = 0 be 5, find the value of λ.

The distance of the point (1, 1, 1) from the origin


We know, distance of (x1, y1, z1) form the origin is :



Putting values of x1, y1, z1= 1


Required Distance = √3


Distance of the point (1, 1, 1) from plane x – y + z + λ = 0


We know, the distance of point (x1,y1,z1) from the plane


is given by:



Putting the necessary values,




According to question, the product of the above two distances is 5



|1 + λ| = 5


1 + λ = 5 or 1 + λ = –5


λ = 4 or λ = –6


9