Suppose `a,b,c in R and a+b+c!=0.` Let `Delta=|(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|.` If `Delta=0,` then

The value of Delta = |(b -c,c -a,a -b),(c -a,a -b,b -c),(a -b,b -c,c -a)| is

Suppose a,b, c epsilon R on abc!=0 . Let Delta=|(1+a,1,1),(1+b,1+2b,1),(1+c,1+c,1+3c)| If Delta=0 , then 1/a+1/b+1/c is equal to

Let a,b and c are real number and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0

Suppose a,b,c are sides of a scalene triangle. Let Delta=|(a,b,c),(b,c,a),(c,a,b)| Then

If a, b and c are real numbers , and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}| Show that either a+b+c=0 or a=b=c

If a,b and c are real numbers, and Delta ={:|( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) |:}=0 Show that either a+b+c=0 "or" a= b= c .