Question

The vector equation of the plane passing through the point $\hat{i}-2\hat{i}+\hat{k}$ and parallel to $3\hat{i}-\hat{j}$, $2\hat{k}-\hat{i}$ is

• A. $\overrightarrow{r}=(\hat{i}-2\hat{i}+\hat{k})+s(3\hat{i}-\hat{i})+t(2\hat{k}-\hat{i})$
• B. $\overrightarrow{r}=(\hat{i}-2\hat{i}+\hat{k})-s(3\hat{i}+\hat{i})-t(2\hat{k}-\hat{i})$
• C. $\overrightarrow{r}=s(\hat{i}-2\hat{i}+\hat{k})-s(3\hat{i}-\hat{i})+t(2\hat{k}-\hat{i})$
• D. $\overrightarrow{r}=t(\hat{i}+2\hat{i}+\hat{k})+s(3\hat{i}-\hat{i})+\hat{t}(2\hat{k}-\hat{i})$

Answer 1

The correct option is A $\overrightarrow{r}=(\hat{i}-2\hat{i}+\hat{k})+s(3\hat{i}-\hat{i})+t(2\hat{k}-\hat{i})$

We know, the vector equation of plane passing through the point $\overrightarrow{a}$ and parallel to $\overrightarrow{b}$ and $\overrightarrow{c}$ is given by,
$\overrightarrow{r}=\overrightarrow{a}+s\overrightarrow{b}+t\overrightarrow{c}$, where $s,t\in R$
Hence the vector equation of the plane passing through the point $i-2i+k$ and parallel to $3i-j$, $2k-i$ is given by,
$\overrightarrow{r}=(i-2i+k)+s(3i-i)+t(2k-i)$