The vector equation of the line passing through the point having position vector $2 \hat{i}+\hat{j}-3…

The vector equation of the line passing through the point having position vector $2 \hat{i}+\hat{j}-3 \hat{k}$ and perpendicular to vectors $\hat{i}+\hat{j}+\widehat{k}$ and $\hat{i}+2 \hat{j}-\widehat{k}$ is
  1. $\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 \hat{j}+\hat{k})$
  2. $\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(\hat{i}+2 \hat{j}-\hat{k})$
  3. $\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}-2 \hat{j}+\hat{k})$
  4. $\bar{r}=(2 \hat{i}+\hat{j}-3 \widehat{k})+\lambda(-3 \hat{i}+2 \hat{j}-\widehat{k})$

Solution

The required equation is $\begin{aligned} & \vec{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k}) \times(\hat{i}+2 \hat{j}-\hat{k}) \\ & \vec{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 j+\hat{k})\end{aligned}$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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