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[" If "bar(p),bar(q),bar(r)" are the vec...

[" If "bar(p),bar(q),bar(r)" are the vectors defined by the relation "],[bar(p)=(bar(b)timesbar(c))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(a)timesbar(c))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)timesbar(b))/([bar(a)bar(b)bar(c)])," where "[bar(a)bar(b)bar(c)]!=0," then "bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r)=...]

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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),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(b)+bar(c)=bar(0) then bar(a)timesbar(b)=

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

(bar(a)+2bar(b)-bar(c))*(bar(a)-bar(b))xx(bar(a)-bar(bar(c)))=

bar(a),bar(b),bar(c) are three non-coplanar vectors. If bar(p)=(bar(b)xxbar(c))/(bar(a)*(bar(b)xxbar(c))),bar(q)=(bar(c)xxbar(a))/(bar(a)*(bar(b)xxbar(c))),bar(r)=(bar(a)xxbar(b))/(bar(a)*(bar(b)xxbar(c))) , show that bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r)=3 .

if bar(a),bar(b),bar(c) are any three vectors then prove that [bar(a),bar(b)+bar(c),bar(a)+bar(b)+bar(c)]=0

(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))=