A ray of light passing through the point A(1,2,3) strikes the plane x+y+z=12 at B and on reflection if passes through C(3,5,9) , then O B is equal to

Step-by-step solution

Let image of point A across x+y+z=12 be Then, equation of line will be aligned p-1 1 & = q-2 1 = r-3 1 = -2(1+2+3-12) 1^2+1^2+1^2 & = 12 3 =4 p-1 1 & =4 p=5 q-2 1 & =4 q=6 r-3 1 & =4 r=7 S(p, q, r) & =S(5,6,7) aligned Now, equation of line C S will be gathered x-5 5-3 = y-6 6-5 = z-7 7-9 x-5 -2 = y-6 -1 = z-7 2 = x=-2 +5, y=6- , z=2 +7 gathered Thus, coordinate of B will be ((-2 +5),(6- ),(2 +7)) Since, B lies on given plane. gathered (-2 +5)+(6- )+(2 +7)=12 =6 gathered array rlrl & & B & =(-7,0,19) & & O B & = (-7