A points P(1,2,3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes. The direction ratios of the line perpendicular to the lines with direction ratios` lt1,-2,2gt` and` lt0,2,1gt `are

Options

A. lt 2,-1,2 gt
B. lt -2,1,2 gt
C. lt 2,1,-2 gt
D. lt -2,-1,-2 gt

Answer

A

Explanation

Let the direction ratios be lt a,b,c gt
`cos90^@=((a)(1)+(b)(-2)+(c)(-2))/(sqrt(a^2+b^2+c^2)sqrt((1)^2+(-2)^2+(-2)^2))`
`a-2b-2c=0 …(1)`
`cos90^@=((a)(0)+(b)(2)+(c)(1))/(sqrt(a^2+b^2+c^2)sqrt((0)^2+(-2)^2+(1)^2))`
`2b+c=0 …(2)`
Form eq. (1) & (2)
`a=-2b, c=-2b`