Let `L_(1)` be the line `vecr_(1)=2hati+hatj-hatk+lamda(hati+2hatk)` and let `L_(2)` be the line `vecr_(2)=3hati+hatj-hatk+mu(hati+hatj+hatk)`. Let `pi` be the plane which contains the line `L_(1)` and is parallel to `L_(2)`. The distance of the plane `pi` from the origin is

Options

A. `sqrt(2//7)`
B. `1//7`
C. `sqrt6`
D. none

Answer

a

Explanation

Equation of the plane containing `L_(1),A(x-2)+B(y-1)+C(z+1)=0`
where `A+2C=0,A+B-C=0`
`impliesA=-2C-,B=3C,C=C`
`implies"Plane is"-2(x-2)+3(y-1)+z+1=0`
or `2x-3y-z-2=0`
Hence, `p=|(-2)/(sqrt14)|=sqrt((2)/(7))`