[bar(a)bar(b)+bar(c)bar(a)+bar(b)+bar(c)]=0

If bar(a),bar(b),bar(c) are coplanar then the value of |[bar(a),bar(b),bar(c)],[bar(a)*bar(a),bar(a)*bar(b),bar(a)*bar(c)],[bar(b).bar(a),bar(b)*bar(b),bar(b)*bar(c)]|=

If [bar(a)bar(b)bar(c)]!=0andbar(p)=(bar(b)xxbar(c))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) , then bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r) is equal to

If bar(a),bar(b),bar(b),bar(c) are three non coplanar vectors bar(p)=(bar(b)xxbar(c))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) then (2bar(a)+3bar(b)+4bar(c))*bar(p)+(2bar(b)+3bar(c)+4bar(a))bar(q)+(2bar(c)+3bar(a)+4bar(b))*bar(r)=

If [bar(a)+2bar(b)2bar(b)+bar(c)5bar(c)+bar(a)]=k[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

The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c) are

The value of [(bar(a)+2bar(b)-bar(c))(bar(a)-bar(b))(bar(a)-bar(b)-bar(c))] is equal to the box product

If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)+bar(b)" "bar(a)+bar(c)" "bar(b)]=[bar(a)" "bar(c)" "bar(b)] (2) [bar(a)-bar(b)" "bar(b)-bar(c)" "bar(c)-bar(a)]=0 .

If bar(b),bar(c) are two unit vectors along the positive x,y axes,and bar(a) is any vector,then (bar(a)*bar(b))bar(b)+(bar(a)*bar(c))bar(c)+(bar(a)*(bar(b)xxbar(c)))/(|bar(b)xxbar(c)|)(bar(b)xxbar(c))=