Question

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

• 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

Answer 1

Answer: (A)

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

Answer 2

It is obvious.