Question

The, position vector of the foot of the $\perp$er drawn from origin to the plane is $4\hat{i}-2\hat{j}-5\hat{k}$ then equation of the plane is

• A. $\overline{r}.(4\hat{i}+2\hat{j}+5\hat{k})=45$
• B. $\overline{r}.(4\hat{i}-2\hat{j}-5\hat{k})=45$
• C. $\overline{r}.(4\hat{i}-2\hat{j}-5\hat{k})+45=0$
• D. $\overline{r}.(4\hat{i}+2\hat{j}-5\hat{k})=37$

Answer 1

The correct option is B $\overline{r}.(4\hat{i}-2\hat{j}-5\hat{k})=45$

Equation of the plane passes through the point $B$ with position vector
$4\hat{i}-2\hat{j}-5\hat{k}and\perp to\overline{OB}=\overline{n}$
$\therefore \overline{n}=\overline{OB}=4\hat{i}-2\hat{j}-5\hat{k}$
$\therefore$ Equation of the plane is $\overline{r}\cdot \overline{n}=\overline{a}\cdot \overline{n}$
$\Rightarrow \overline{r}\cdot (4\hat{i}-2\hat{j}-5\hat{k})=(4\hat{i}-2\hat{j}-5\hat{k})\cdot (4\hat{i}-2\hat{j}-5\hat{k})$
$\Rightarrow \overline{r}\cdot (4\hat{i}-2\hat{j}-5\hat{k})=45$
Hence (B) is correct choice.