MHT CET · Maths · Three Dimensional Geometry
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
- A \(\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 \hat{j}+\hat{k})\)
- B \(\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(\hat{i}+2 \hat{j}-\hat{k})\)
- C \(\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}-2 \hat{j}+\hat{k})\)
- D \(\bar{r}=(2 \hat{i}+\hat{j}-3 \widehat{k})+\lambda(-3 \hat{i}+2 \hat{j}-\widehat{k})\)
Answer & Solution
Correct Answer
(A) \(\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 \hat{j}+\hat{k})\)
Step-by-step Solution
Detailed explanation
The required equation is
\(\begin{aligned} & \vec{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k}) \times(\hat{i}+2 \hat{j}-\hat{k}) \\ & \vec{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 j+\hat{k})\end{aligned}\)
\(\begin{aligned} & \vec{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k}) \times(\hat{i}+2 \hat{j}-\hat{k}) \\ & \vec{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 j+\hat{k})\end{aligned}\)
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