The angle between the pair of planes represented by equation `2x^2-2y^2+4z^2+6xz+2yz+3xy=0` is

Options

A. `cos^(-1)(1/3)`
B. `cos^(-1)(4/21)`
C. `cos^(-1)(4/9)`
D. `cos^(-1)(7sqrt(84))`

Answer

C

Explanation

`2x^(2)-2y^(2)+4z^(2)+6xz+2yz+3xy=0`
or `2x^(2)+x(6z++3y)-2y^(2)+4z^(2)+2yz=0`
`therefore x=(-6z+3y)+-sqrt(36z^(2)+9y^(2)+36yz-8(-2y^(2)+4z^(2)+2yz))/(4)`
`therefore x=((-6z+3y)+-sqrt((2x+5y)^(2)))/(4)`
`therefore x= ((-6z+3y)+-(2z+5y))/(4)`
or `2x-y+2z=0, x+2y+2z=0`
`therefore` Angle between planes
`therefore =cos^(-1)((2)(1)+(-1)(2)+(2)(2))/sqrt(((2)^(2)+(-1)^(2)(2)^(2))sqrt((1)^(2)+(2)^(2)+(2)^(2)))`
`=cos^(-1)(4/9)`