If `[bar abar b bar c]=-4` then the volume of the parallelopiped with coterminus edges `bara+2 bar b,2 bar b+bar c,3bar c+bar a` is (in cu units)

Derive the expression for the volume of the prallelopiped whose coterminus edges are vectors bar(a),bar(b),bar(c) .

If |[bar(a).bar(a), bar(a).bar(b),bar(a).bar(c)], [bar(a).bar(b), bar(b).bar(b), bar(b).bar(c)], [bar(a).bar(c), bar(b).bar(c), bar(c).bar(c)]| =144 then the volume of tetrahedron formed with coterminous edges bar(a) ,bar(b) and bar(c) is equal to

If volume of parallelopiped determined by bar(a),bar(b),bar(c) is 5, then the volume of parallelopiped determined by 2bar(a)+bar(b)+2bar(c),bar(a)-bar(b)-2bar(c),3bar(a)+bar(b)-6bar(c)

The volume of parallelopiped with vector bara+2barb-barc,bara-barb and bara-barb-barc is equal to k[bar(a)bar(b)bar(c)] then k=

The volume of parallelopiped with vector bara+2barb-barc,bara-barb and bara-barb-barc is equal to k[bar(a)bar(b)bar(c)] then k=

bar(a),bar(b) and bar( c ) are three non zero, non planar vectors. bar(p)=bar(a)+bar(b)-2bar( c ),bar(q)=3bar(a)-2bar(b)+bar( c ) and bar( r )=bar(a)-4bar(b)+2bar( c ) . The volume of the parallelepiped formed by the vectors bar(a),bar(b) and bar( c ) is V_(1) and the volume of the parallelepiped formed by the vectors bar(p),bar(q) and bar( r ) is V_(2) then V_(2):V_(1) = .............

let bar(a),bar(b)&bar(c) be three non-zero non coplanar vectors and bar(p),bar(q)&bar(r) be three vectors defined as bar(p)=bar(a)+bar(b)-2bar(c);bar(q)=3bar(a)-2bar(b)+bar(c)&bar(r)=bar(a)-4bar(b)+2bar(c) .If v_(1),v_(2) are the volumes of parallelopiped determined by the vectors bar(a),bar(b),bar(c) and bar(p),bar(q),bar(r) respectively then v_(2):v_(1) is

Let bar(a),b,bar(c) are three vectors such that , |bar(a)|=|bar(b)|=|bar(c)|=2 and (bar(a),bar(b))=(pi)/(3)=(bar(b),bar(c))=(bar(c),bar(a)) The volume of the parallelepiped whose adjacent edges are 2bar(a),3bar(b),4bar(c)

If bar(a),bar(b),bar(c) are three coterminous edges of a parallelopiped of volume 6 then value of [bar(a)timesbar(b)quad bar(a)timesbar(c)quad bar(b)timesbar(c)]=