What is the angle between the plane `2x-y+z=6 and x+y+2z=3`?

Options

A. `pi//2`
B. `pi//3`
C. `pi//4`
D. `pi//6`

Answer

B

Explanation

We know, if
`a_1x+b_1y+c_1z=d_1` and
`a_2x+b_2y+c_2z=d_2`
are two planes then angle between them is
`costheta=(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))`
Let `theta` be the angle between given planes
Here, `a_1=2,b_1=-1,c_1=1`
`a_2=1,b_2=1,c_2=2`
`:. cos theta=(2xx1+1xx(-1)+1xx2)/(sqrt(4+1+1)sqrt(1+1+4))`
`=3/6=1/2=cos. pi/3`
`rArr theta=pi/3`