Prove that identities: `|[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=(a b+b c+a c)^3`

Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab, -ab]|=(ab+bc+ca)^2

If the given vectors (-bc,b^2+bc,c^2+bc)(a^2+ac,-ac,c^2+ac) and (a^2+ab,b^2+ab,-ab) are coplanar, where none of a,b and c is zero then

| [-bc, b ^ (2) + bc, c ^ (2) + bca ^ (2) + ac, -ac, c ^ (2) + aca ^ (2) + ab, b ^ (2) + ab, -ab (ab + bc + ac), is = 64. then

Prove that det[[b^(2)-ab,b-c,bc-acab-a^(2),a-b,b^(2)-abbc-ac,c-a,ab-a^(2)]]=0

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

Using properties of determinants, show the following: |[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3