Question

Equation of plane passing through points given by position vectors $\overline{a}and\overline{b}$ and origin will be

• A. $\overline{r}.\frac{\overline{a}-\overline{b}}{|\overline{a}\times \overline{b}|}=0.$
• B. $\overline{r}.\frac{\overline{a}+\overline{b}}{|\overline{a}\times \overline{b}|}=0.$
• C. $\overline{r}.\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}=0.$
• D. $\overline{r}.\left(\frac{\overline{a}.\overline{b}}{|\overline{a}\times \overline{b}|}\right)=0.$

Answer 1

The correct option is C

$\overline{r}.\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}=0.$

Here we know given the plane passes through points given by position vectors $\overline{a}and\overline{b}$ . So the perpendicular to the plane will be along $\overline{a}\times \overline{b}$. Therefore our $\hat{n}$ or unit vector perpendicular to the plane will be $\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}$. Equation of plane will be

$(\overline{r}-0).\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}=0.$

Which is same as,

$\overline{r}.\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}=0.$