If the vectors $\vec{d}=\vec{i}+a \vec{j}+a^2 \vec{k}, \vec{b}=\vec{i}+b \vec{j}+b^2 \vec{k}, \vec{c

Question

If the vectors $\vec{d}=\vec{i}+a \vec{j}+a^2 \vec{k}, \vec{b}=\vec{i}+b \vec{j}+b^2 \vec{k}, \vec{c}=\vec{i}+c \vec{j}+c^2 \vec{k}$ are three mon-coplanar veclose and $\left.\left|\begin{array}{ll}a & d^2\end{array} 1+a^3ight| \begin{array}{cc}b & 1+b^3 \ c & c^2\end{array} 1+c^3 ightvert\,=0$, then the value of $a b c$ is

Professor PC Thomas Classes · Answer

Determinant properties.