Let `Delta_1=[[ap^2,2ap,1],[aq^2,2aq,1],[ar^2,2ar,1]]` and `Delta_2=[[apq,a(p+q),1],[aqr,a(q+r),1],[arp,a(r+p),1]]` then

Let Delta_(1)=|(ap^(2),2ap,1),(aq^(2),2aq,1),(ar^(2),2ar,1)|andDelta_(2)=|(apq,a(p+q),1),(aqr,a(q+r),1),(arp,a(r+p),1)| then a) Delta_(1)= Delta_(2) b) Delta_(2)=2Delta_(1) c) Delta_(1) = 2Delta_(2) d) Delta_(1) +2Delta_(2) = 0

Let Delta_(1)=|{:(ap^(2),2ap,1),(aq^(2),2aq,1),(ar^(2),2ar,1):}| and Delta_(2)=|{:(apq,a(p+q),1),(aqr,a(q+r),1),(arp,a(r+p),1):}| then

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expending or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expanding or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

. 1/(p+q),1/(q+r),1/(r+p) are in AP, then

If a_(1),a_(2),a_(3),…. are in A.P., then a_(p),a_(q),q_(r) are in A.P. if p,q,r are in

If a_(1),a_(2),a_(3),…. are in A.P., then a_(p),a_(q),q_(r) are in A.P. if p,q,r are in

If a_(1),a_(2),a_(3),…. are in A.P., then a_(p),a_(q),a_(r) are in A.P. if p,q,r are in