Matrices and Determinants
651 Questions
Start JEE Mains Test
1985
Q651
JEE Advanced
Numerical
14 Mar 2026
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 the vectors
$\overrightarrow A = \left( {1,a,{a^2}} \right),\,\,\overrightarrow B = \left( {1,b,{b^2}} \right),\,\,\overrightarrow C = \left( {1,c,{c^2}} \right),$ are non-coplannar, then the product $abc=$ .......
$\overrightarrow A = \left( {1,a,{a^2}} \right),\,\,\overrightarrow B = \left( {1,b,{b^2}} \right),\,\,\overrightarrow C = \left( {1,c,{c^2}} \right),$ are non-coplannar, then the product $abc=$ .......
Correct Answer: $$-1$$