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Line and Plane — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsLine and Plane3 Marks
Question
Find the vector equation of the line passing through the point having position vector

$3 \hat{i}+4 \hat{j}-7 \hat{k}$ and parallel to $6 \hat{i}-\hat{j}+\hat{k}$.

✓

Answer

The vector equation of the line passing through $A(\bar{a})$ and parallel to the vector $\bar{b}$ is

$\overline{\mathrm{r}}=\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}}$, where $\lambda$ is a scalar.

∴ the vector equation of the line passing through the point having position vector

$3 \hat{i}+4 \hat{j}-7 \hat{k}$ and parallel to the vector $6 \hat{i}-\hat{j}+\hat{k}$ is

$\overline{\mathrm{r}}=(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-7 \hat{\mathrm{k}})+\lambda(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$

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