Question

If $r\cdot a=r\cdot b=r\cdot c=0$ where a, b, c are noncoplanar, then?

• A. $r\perp c\times a$
• B. $r\perp a\times b$
• C. $r\perp b\times c$
• D. $r=0$

Answer 1

The correct option is D $r=0$

$\overline{r}.\overline{a}=\overline{r}.\overline{b}=\overline{r}.\overline{c}=0$

Hence,we can say that either $\overline{r}$ is perpendicular to all $\overline{a},\overline{b}and\overline{c}$ or $\overline{r}=\overline{0}.$

Now,possibility of $\overline{r}$ being perpendicular to $\overline{a},\overline{b}and\overline{c}$ is not there because $\overline{a},\overline{b}and\overline{c}$ are non coplanar and$\overline{r}$can't be perpendicular to two different planes at the same time.

$\therefore \overline{r}=\overline{0}and\left|\overline{r}\right|=0$

$\therefore D)Answer.$