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Straight line in space — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsStraight line in space3 Marks
Question
Find the vector equation of a line passing through (2, -1, 1) and parallel to the line whose equations are $\frac{\text{x}-3}{2}=\frac{\text{y}+1}{7}=\frac{\text{z}-2}{-3}.$
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Answer

We know that the vector equation of a line passing through a point with position vector $\vec{\text{a}}$ and parallel to the vector $\vec{\text{b}}$ is $\vec{\text{r}}=\vec{\text{a}}+\lambda\vec{\text{b}}$
Here,
$\vec{\text{a}}=2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$
$\vec{\text{b}}=2\hat{\text{i}}+7\hat{\text{j}}-3\hat{\text{k}}$
Vector equation of the required line is
$\vec{\text{r}}=\big(2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}\big)+\lambda\big(2\hat{\text{i}}+7\hat{\text{j}}-3\hat{\text{k}}\big)$
Here, $\lambda$ is a parameter.

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