If `|{:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3)):}|=0` and vectors `(1,a,a^(2)),(1,b,b^(2))` and `(1,c,c^(2))` are non-coplanar, then the product abc equal to:

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^3)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are non coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^2)|=0 and vectors (1,a,a^2),(1,b,b^2) and (1,c,c^2) are hon coplanar then the product abc equals (A) 2 (B) -1 (C) 1 (D) 0

If a,b, and c are all different and if |{:(a,a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3)):}| =0 Prove that abc =-1.

If a,b,c are distinct real numbers and |{:(a,a^(2),a^(3)-1),(b,b^(2),b^(3)-1),(c,c^(2),c^(3)-1):}|=0 then

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| = |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Show that a^(2)(1+b^(2))+b^(2)(1+c^(2))+c^(2)(1+a^(2))gt abc

p=2a-3b,q=a-2b+c and r=-3a+b+2c , where a,b,c being non-coplanar vectors, then the vector -2a+3b-c is equal to

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

If a_(1)^(2)+a_(2)^(2)+a_(3)^(2)=1, b_(1)^(2)+b_(2)^(2)+b_(3)^(2)=4, c_(1)^(2)+c_(2)^(2)+c_3^(2)=9, a_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3)=0, a_(1)c_(1)+a_(2)c_(2)+a_(3)c_(3)=0, b_(1)c_(1)+b_(2)c_(2)+b_(3)c_(3)=0 and A[(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))] , then |A|^(4) is equal to

Show that the vectors a-2b+4c,-2a+3b-6c and -b+2c are coplanar vector, where a,b,c are non-coplanar vectors.