The direction ratios of the normal to the plane passing through origin and the line of intersection of the planes x+2y+3z=4 and 4x+3y+2z=1 are . . .

Options

A. 2,3,1
B. 1,2,3
C. 3,1,2
D. 3,2,1

Answer

D

Explanation

We have, line of intersection of the planes
`x+2y+3z=4 and 4x+3y+2z=1`
`therefore`Equation of plane passing through the given planes is
`(x+2y+3z-4)+lamda(4x+3y+2z-1)=0`
`implies(1+4lamda)x+(2+3lamda)y+(3+2lamda)+(-4-lamda)=0`
Since, plane passing through origin
`therefore-4-lamda=0implieslamda=-4`
Now, equation of plane is
`(1-16)x+(2-12)y+(3-8)z+0=0`
`implies-15x-10y-5z=0`
`implies3x+2y+z=0`
`therefore`Direction ratios of the normal to the plane are 3,2,1.