The vectors `bara,barb and bara+barb` are

For any three vectors bara,barb and barc,(bara-barb)[(barb+barc)xx(barc+bara)] is equal to:

For any three vectors bara,barb and barc,(bara-barb) .[(barb+barc)xx(barc+bara)] is equal to:

The position vector of the point which divides the join of points with position vectors bara+barb and 2 bara - barb in the ratio 1:2 is

If theta is the angle between any two vectors bara and barb and | bara xx barb | = | bara.barb | , then value of theta is

If bara and barb are unit vectors such that bara + 2barb and 5bara- 4barb are perpendicular to each other, then the angle between bara and barb is

For the unit vectors bara and barb if bara + barb = bar0 , then what is bara. barb ?

The volume of parallelopiped with vectors bara+2barb-barc,bara-barb,bara-barb-barc as coterminous edges is K[bara barb barc] then abs(K) =