`(bar(a)-bar(d))*(bar(b)-bar(c))+(bar(b)-bar(d))*(bar(c)-bar(a))+(bar(c)-bar(d))*(bar(a)-bar(b))=`

(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(d) is unit vector such that bar(d)=(bar(b)xxbar(c))+u=(bar(c)xx^(-))+v=(bar(a)xxbar(b)))|(bar(d)*bar(a))(bar(b)xxbar(c))+(bar(d)*bar(b))(bar(c)xxbar(a))+(bar(d)*bar(c))(bar(a)xxbar(b))| is equal to

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

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

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)]=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(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) are position vectors of vertices A,B,C of Delta ABC. If bar(r) is position vector of apoint P such that (|bar(b)-bar(c)|+|bar(c)-bar(a)|+|bar(a)-bar(b)|)bar(r)=|bar(b)-bar(c)|bar(a)+|bar(c)-bar(a)|bar(b)+|bar(a)-bar(b)|bar(c) then the point P is