Question

The equation if the plane passing through the point (2,-1,3) and perpendicular to the vector $3\hat{i}+2\hat{j}-\hat{k}$ is:

• A. $\overline{r}(3\hat{i}+2\hat{j}-\hat{k}=1$
• B. $\overline{r}(3\hat{i}+2\hat{j}-\hat{k}+1=0$
• C. $\overline{r}(3\hat{i}+2\hat{j}-\hat{k}=0$
• D. $\overline{r}(3\hat{i}+2\hat{j}+\hat{k}=1$

Answer 1

The correct option is A $\overline{r}(3\hat{i}+2\hat{j}-\hat{k}=1$

The plane passes through $(2,-1,3)$ and is perpendicular to vector $3\hat{i}+2\hat{j}-\hat{k}$

$\therefore$Equation of plane is

$3x+2y-z=d$ passes through $2,-1,3$

$\therefore 3\times 2+2\times -1-3=d$

$\Rightarrow 6-2-3=d\Rightarrow 6-5=d$

$d=1$

$\therefore$Equation of plane is

$\overrightarrow{r}(3\hat{i}+2\hat{j}-\hat{k})=1$