question_answer

For any three non-zero vectors \[{{r}_{1}},\,{{r}_{2}}\] and \[{{r}_{3}}\], \[\left| \,\begin{matrix}    {{r}_{1}}\,.\,{{r}_{1}} & {{r}_{1}}\,.\,{{r}_{2}} & {{r}_{1}}\,.\,{{r}_{3}}  \\    {{r}_{2}}\,.\,{{r}_{1}} & {{r}_{2}}\,.\,{{r}_{2}} & {{r}_{2}}\,.\,{{r}_{3}}  \\    {{r}_{3}}\,.\,{{r}_{1}} & {{r}_{3}}\,.\,{{r}_{2}} & {{r}_{3}}\,.\,{{r}_{3}}  \\ \end{matrix} \right|=0\]. Then which of the following is false                                    [AMU 2000]

A)             All the three vectors are parallel to one and the same plane

B)             All the three vectors are linearly dependent

C)             This system of equation has a non-trivial solution

D)             All the three vectors are perpendicular to each other