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

[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)]|=

bar(a),bar(b),bar(c) are three unit vectors such that bar(a)xx(bar(b)xxbar(c))(1)/(2)bar(b), then (bar(a),bar(b))=(bar(a),bar(c))=(bar(b),bar(c)), are non-collinear)

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)]=1 then (bar(a)(bar(b)xxbar(c)))/((bar(c)xxbar(a))*bar(b))+(bar(b)*(bar(c)xxbar(a)))/((bar(a)xxbar(b))*bar(c))+(bar(c)(bar(a)xxbar(b)))/((bar(b)xxbar(c))*bar(a))

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(p)bar(q)bar(r) is reciprocal system of vector triad bar(a),bar(b) and bar(c) then [bar(a)bar(b)bar(c)][bar(p)bar(q)bar(r)]=

(bar(a)+bar(b))xx(bar(a)-bar(b))+(bar(b)-bar(c))xx(bar(b)-bar(c))+(bar(c)+bar(a))(bar(c)-bar(a))=

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