Let `L_(1):bar(r)=(i-j)+t_(1)(2i+3j+k),L_(2):bar(r)=(-i+2j+2k)+t_(2)(5i+j)`, then The distance of origin from the plane passing through the point (1,-1,1) and whose normal is perpendicular to both `L_(1) and L_(2)` is

Let L_(1):bar(r)=(i-j)+t_(1)(2i+3j+k), L_(2):bar(r)=(-i+2j+2k)+t_(2)(5i+j) , then The shortest distance between L_(1) and L_(2) is

Let L_(1):bar(r)=(i-j)+t_(1)(2i+3j+k) ,L_(2):bar(r)=(-i+2j+2k)+t_(2)(5i+j) ,then The shortest distance between L_(1) and L_(2) is

Equation of the plane passing through the points i+j-2k,2i-j+kandi+2j+k is

The perpendicular distance from origin to the plane passing through the pooints 2i+j+3k,i+3j+2k,3i+2j+k is

A line L_1 passing through a point with position vector p=i+2h+3k and parallel a=i+2j+3k , Another line L_2 passing through a point with direction vector to b=3i+j+2k . Q. The minimum distance of origin from the plane passing through the point with position vector p and perpendicular to the line L_2 , is

Equation of plane passing through (1,0,1),(3,1,2) and parallel to the vector i-j+2k is

The perpendicular distance from origin tot plane passing through the points 2bar(i)-2bar(j)+bar(k),3vec i+2bar(j)-bar(k),3vec i-bar(j)-2bar(k) is

The vector equation of the plane passing through the points bar(i)-2bar(j)+bar(k),3bar(k)-2bar(j) and parallel to the vector 2bar(i)+bar(j)+bar(k) is