`bar(a)*{(bar(b)+bar(c))times(bar(a)+bar(b)+bar(c))}=......`,

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

If [(bar(a)+2bar(b)+3bar(c))times(bar(b)+2bar(c)+3bar(a))].(bar(c)+2bar(a)+3bar(b))=54 , where bar(a),bar(b)&bar(c) are 3 non coplanar vectors then |[bar(a).bar(a)quad bar(a).bar(b)quad bar(a).bar(c)],[bar(b).bar(a)quad bar(b).bar(b)quad bar(b).bar(c)],[bar(c).bar(a)quad bar(c).bar(b)quad bar(c).bar(c)]|

([[bar(a),bar(b),bar(c)]])/([[bar(b),bar(a),bar(c)]]) =

(bar(a)times(bar(b)+bar(c))+bar(b)times(bar(c)+bar(a))+bar(c)times(bar(a)+bar(b)))*(bar(a)timesbar(b))|= (A) |bar(b)timesbar(c)| (B) |bar(c)timesbar(a)| (C) |bar(a)timesbar(b)+bar(b)timesbar(c)+(bar(c)timesbar(a))| (D) 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))=

If bar(a), bar(b), bar(c) form a left handed orthogonal system and bar(a)*bar(a)=4, bar(b)*bar(b)=9, bar(c)*bar(c)=16 then [bar(a) bar(b) bar(c)] =

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),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)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(c) are non-zero,non-coplanar vectors then {bar(a)times(bar(b)+bar(c))}times{bar(b)times(bar(c)-bar(a))} is collinear with the vector