Let `L_1` be the line ` vec r_1=2 hat i+ hat j- hat k+lambda(i+1 hat k)` and let `L_2` be the line ` vec r_2=3 hat i+ hat j+mu(i+ hat j- hat k)` . Let `pi` be the plane which contains the line `L_1` and is parallel to `L_2dot` The distance of the plane `pi` from the origin is a. `sqrt(6)` b. `1//7` c. `sqrt(2//7)` d. none of these

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))`