For any three non-zero vectors ${\overrightarrow{\mathbf{r}}}_{1}{\overrightarrow{\mathbf{r}}}_{2}$ and ${\overrightarrow{\mathbf{r}}}_{3}$, $\left| \begin{matrix} {\overrightarrow{\mathbf{r}}}_{1} \bullet {\overrightarrow{\mathbf{r}}}_{1} & {\overrightarrow{\mathbf{r}}}_{1} \bullet {\overrightarrow{\mathbf{r}}}_{2} & {\overrightarrow{\mathbf{r}}}_{1} \bullet {\overrightarrow{\mathbf{r}}}_{3} \ {\overrightarrow{\mathbf{r}}}_{2} \bullet {\overrightarrow{\mathbf{r}}}_{1} & {\overrightarrow{\mathbf{r}}}_{2} \bullet {\overrightarrow{\mathbf{r}}}_{2} & {\overrightarrow{\mathbf{r}}}_{2} \bullet {\overrightarrow{\mathbf{r}}}_{3} \ {\overrightarrow{\mathbf{r}}}_{3} \bullet {\overrightarrow{\mathbf{r}}}_{1} & {\overrightarrow{\mathbf{r}}}_{3} \bullet {\overrightarrow{\mathbf{r}}}_{2} & {\overrightarrow{\mathbf{r}}}_{3} \bullet {\overrightarrow{\mathbf{r}}}_{3} \end{matrix} ight| = 0$ , Then, which of the following is false?

Question

For any three non-zero vectors ${\overrightarrow{\mathbf{r}}}_{1}{\overrightarrow{\mathbf{r}}}_{2}$ and ${\overrightarrow{\mathbf{r}}}_{3}$, $\left| \begin{matrix} {\overrightarrow{\mathbf{r}}}_{1} \bullet {\overrightarrow{\mathbf{r}}}_{1} & {\overrightarrow{\mathbf{r}}}_{1} \bullet {\overrightarrow{\mathbf{r}}}_{2} & {\overrightarrow{\mathbf{r}}}_{1} \bullet {\overrightarrow{\mathbf{r}}}_{3} \ {\overrightarrow{\mathbf{r}}}_{2} \bullet {\overrightarrow{\mathbf{r}}}_{1} & {\overrightarrow{\mathbf{r}}}_{2} \bullet {\overrightarrow{\mathbf{r}}}_{2} & {\overrightarrow{\mathbf{r}}}_{2} \bullet {\overrightarrow{\mathbf{r}}}_{3} \ {\overrightarrow{\mathbf{r}}}_{3} \bullet {\overrightarrow{\mathbf{r}}}_{1} & {\overrightarrow{\mathbf{r}}}_{3} \bullet {\overrightarrow{\mathbf{r}}}_{2} & {\overrightarrow{\mathbf{r}}}_{3} \bullet {\overrightarrow{\mathbf{r}}}_{3} \end{matrix} ight| = 0$ , Then, which of the following is false?

Dr. Abubacker · Accepted Answer

The correct answer is Option A: All the three vectors are parallel to one and the same plane.

Explanation

Reviewed by Dr. Abubacker

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