If $$\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {{c^2}} & {1 + {c^3}} \cr } } \right| = 0$ and vectors $\left( {1,a,{a^2}} \right),\,\,$$ $\left( {1,b,{b^2}} \right)$ and $\left( {1,c,{c^2}} \right)\,$ are non-coplanar, then the product $abc$ equals :

Question

If $$\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {{c^2}} & {1 + {c^3}} \cr } } \right| = 0$ and vectors $\left( {1,a,{a^2}} \right),\,\,$$

$\left( {1,b,{b^2}} \right)$ and $\left( {1,c,{c^2}} \right)\,$ are non-coplanar, then the product $abc$ equals :

$0$

$2$

$-1$

$1$

Solution

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