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Line and Plane — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsLine and Plane1 Mark
Question
Find the vector equation of the line passing through the point having position vector $4 \hat{i}-\hat{j}+2 \hat{k}$ and parallel to vector $-2 \hat{i}-\hat{j}+\hat{k}$
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Answer

The equation of the line passing through $\mathrm{A}(\bar{a})$ and parallel to vector $\bar{b}$ is $\bar{r}=\bar{a}+\lambda \bar{b}$. The equation of the line passing through $4 \hat{i}-\hat{j}+2 \hat{k}$ and parallel to vector $-2 \hat{i}-\hat{j}+\hat{k}$ is $\bar{r}=(4 \hat{\imath}-\hat{j}+2 \hat{k})+\lambda(-2 \hat{i}-\hat{j}+\hat{k})$.

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