The acute angle between the planes `2x-y+z=6` and `x+y=2z=3` is

Options

A. `pi//5`
B. `pi//4`
C. `pi//6`
D. `pi//3`

Answer

D

Explanation

The given equation of the planes are `x+y+2z=3and -2x+y-z=11`.
We know that, the angle between the planes
`a_1x+b_1y+c_1z+d_1=0`
`and a_2x+b_2y+c_2z+d_2=0` is given by
`cos theta =abs((a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2)sqrt(a_2^2+b_2^2+c_2^2)))`
Here, `a_1=1,b_1=1,c_1=2,a_2=-2,b_2=1,c_2=-1`
`:. costheta=abs((1xx(-2)+1xx1+2xx(-1))/(sqrt(1+1+4)sqrt(4+1+1)))`
`=abs((-2+1-2)/(sqrt6sqrt6))=abs(3/6)=1/2=cos.pi/3rArrtheta=pi/3`