The angles between the planes `vecr.(3hati-6hatj+2hatk)=4` and `vecr.(2hati-hatj+2hatk)=3`, is

Options

A. `cos^(-1)(16/21)`
B. `cos^(-1)(4/21)`
C. `cos^(-1)(3/4)`
D. `cos^(-1)(1/4)`

Answer

a

Explanation

The given planes are `3x-6y+2z=4` and `2x-y+2z=3`.
`therefore costheta=|(3 xx 2)+(-6) xx (-1) +(2 xx 2)|/(sqrt(3^(2)+(-6)^(2)+2^(2))sqrt(2^(2)+(-1)^(2)+2^(2))`
`16/(sqrt(49)sqrt(9))=16/(7 xx 3) =16/21`.
`rArr theta=cos^(-1)(16/21)`.