If the shortest distance between the lines `barr=(bari +barj-bark)+s(2bari +barj+lamdabark)` and `barr = (2bari +bark)+t(bari + barj +bark)` is zero find the value of `lamda`.

The shortest distance between the skew lines barr=(bari+3barj+3barK)+t(bari+3barj+2bark) and barr=(4bari+5barj+6bark)+t(2bari+3barj+bark) is

The shortest distance between the lines whose equations are barr = t ( bari + barj + bark ), barr = bark + s(bari - bar2j + 3bark) is

The angle between the planes barr.(2bari+barj+bark)=5, (bari-barj+2bark)=3 is

The cosine of the angle between the lines barr=(3bari+2barj-4bark+t(bari+2barj+2bark), barr=(5bari-2bark)+bars(3bari+2barj+6bark) is

Angle between the line barr = (-bari+3barj+3bark)+t(2bari+3barj+6bark) " and the plane " barr.(-bari+barj+bark) = 5 is

The angle between the line barr=(2bari-barj+bark)+lambda(bari-barj+bark) and the plane barr.(3bari+2barj-bark)=4 is

The lines barr= bari- barj +lambda(2 bari+bark) and bar=(2bari-barj) +mu (bari+barj-bark) intersect for

Observe the following, choose correct answer : Assertion(A): The lines barr =(2bari + barj)+s(bari + barj -bark) and barr =(bari +bark)+t(7bari - barj +bark) are coplanar. Reason (R) : Condition for the lines barr = bara + sbarb and barr = barc + tbard to be coplanar is [bara-barc barb -bard]=0

The angle between the lines barr=(2bari-3barJ+k)+lamda(bari+4barj+3k) and (barI-barj+2k)+mu(bari+2barj-3k) is