Question

The image of the point (2, -1,5) in the plane r . i = 0 is
(A) (-2,-1,5)
(B) (2,1,-5)
(C) (-2,1,-5)
(D) (2,0,0)​

Answer 1

Answer:

I think option C is the answer

Answer 2

Coordinates of image is ( -2 , -1 , 5 )

Option A is correct

•Equation of plane is r . i = 0

i.e. x = 0

•It is equation of Y-Z plane

•Let PQ be the line Perpendicular to the plane from (2, -1,5)

•Also line is perpendicular to plane so direction ratios of line will be that of the DR's of plane

•equation of line will be :

(x-2)/(1) = (x-b)/0 = (x-c)/0 = k say

•General points of line PQ will be

x = k + 2

y = -1

z = 5

•Also , this line intersect the plane

so, foot of perpendicular will be

(k +2) = 0

k = -2

•Hence foot of perpendicular will be (0 , -1 , 5 )

•let coordinates of image is ( e , f , g )

By mid-point theorm

0 =( 2 + e )/2 => e = -2

-1 = ( -1 + f )/2 => f = -1

5 = ( 5 + g )/2 => g = 5

•so , coordinates of image is

( -2 , -1 , 5 )