Angle between the two planes of which one plane is `4x +y + 2z=0` and another plane containing the lines `(x- 3)/2=(y-2)/3=(z-1)/lambda, (x-2)/3=(y-3)/2=(z-2)/3`

Options

A. `pi/3`
B. `pi/2`
C. `pi/6`
D. `(2pi)/3`

Answer

B

Explanation

Lines `(x-3)/2 = (y-2)/3=(z-1)/lambda, (x-2)/3,(y-3)/2,=(z-2)/3`
must be coplanar.
`rArr |{:(2,3,lambda),(3,2,3),(1,-1,-1):}|=0`
`rArr lambda=4`
`therefore` Equation of plane is `|{:(x-3,y-2,z-1),(3,2,3):}|=0`
or `x+6y-5z=10` …....(1)
Equation of given plane is `4x+y+2z=0`..........(2)
Angle between the plane i.e, `theta` is given by
`costheta=(4(1)+6(1)-5(2))/(sqrt(1+36+15)sqrt(16+1+4))=0`
`rArr theta=90^(@)`