The value of a so that volume of parallelopiped formed by vectors `overset(^)i+a overset(^)j+overset(^)k,overset(^)j+a overset(^)k,aoverset(^)i+.overset(^)k` becomes minimum is

If the vectors 3overset(^)i+overset(^)j-5overset(^)k and aoverset(^)i+boverset(^)j-15overset(^)k are collinear, if

If the vectors 3overset(^)i+overset(^)j-5overset(^)k and aoverset(^)i+boverset(^)j-15overset(^)k are collinear, if

If the vectors overset(^)i+2overset(^)k,overset(^)j+overset(^)k and lambda overset(^)i+mu overset(^)j collinear, then

If the vectors overset(^)i+2overset(^)k,overset(^)j+overset(^)k and lambda overset(^)i+mu overset(^)j collinear, then

If the volume of parallelopiped with coterminus edges -poverset(^)i+5k,overset(^)i-overset(^)j+qoverset(^)k and 3overset(^)i-5overset(^)j is 8 then

If the volume of parallelopiped with coterminus edges -poverset(^)i+5k,overset(^)i-overset(^)j+qoverset(^)k and 3overset(^)i-5overset(^)j is 8 then

If vectors overset(^)i+overset(^)j+overset(^)k,overset(^)j-overset(^)i,overset(^)i+2overset(^)j+aoverset(^)k are coplanar, then a is equal to

If vectors overset(^)i+overset(^)j+overset(^)k,overset(^)j-overset(^)i,overset(^)i+2overset(^)j+aoverset(^)k are coplanar, then a is equal to

Three concurrent edges OA,OB,OC of a parallelopiped are represented by three vectors 2overset(^)i+overset(^)j-overset(^)k,overset(^)i+2overset(^)j+3overset(^)k and -3overset(^)i-overset(^)j+overset(^)k the volume of the solid so formed in cubic unit is

Three concurrent edges OA,OB,OC of a parallelopiped are represented by three vectors 2overset(^)i+overset(^)j-overset(^)k,overset(^)i+2overset(^)j+3overset(^)k and -3overset(^)i-overset(^)j+overset(^)k the volume of the solid so formed in cubic unit is