Find the vector equation of the line passing through the point ha… - Vidyadip

Question

Find the vector equation of the line passing through the point having position vector $4 \hat{ i }-\hat{ j }+2 \widehat{ k }$ and parallel to the vector $-2 \hat{ i }-\hat{ j }+\widehat{ k }$

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Answer

The vector equation of a line passing through a point with position vector $\overline{ a }$ and parallel to $\overline{ b }$ is $\overline{ r }=\overline{ a }+\lambda \overline{ b }$.
$\therefore$ The vector equation of the line passing through the point having position vector $4 \hat{ i }-\hat{ j }+2 \widehat{ k }$ and parallel to the vector $-2 \hat{ i }-\hat{ j }+\widehat{ k }$ is $\overline{ r }=(4 \hat{ i }-\hat{ j }+2 \widehat{ k })+\lambda(-2 \hat{ i }-\hat{ j }+\widehat{ k })$

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