JEE Main 2003Annual, Paper 1MathematicsMediumVector Algebra184× since 2002If ∣aa21+a3bb21+b3cc21+c3∣=0\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {{c^2}} & {1 + {c^3}} \cr } } \right| = 0abca2b2c21+a31+b31+c3=0 and vectors (1,a,a2), \left( {1,a,{a^2}} \right),\,\,(1,a,a2), (1,b,b2)\left( {1,b,{b^2}} \right)(1,b,b2) and (1,c,c2) \left( {1,c,{c^2}} \right)\,(1,c,c2) are non-coplanar, then the product abcabcabc equals :AOption A. 000BOption B. 222COption C. −1-1−1DOption D. 111CheckSkip · show solution
