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Question
Find the equation of the line passing through the point (2, −1, 3) and parallel to the line \[\overrightarrow{r} = \left( \hat{i} - 2 \hat{j} + \hat{k} \right) + \lambda\left( 2 \hat{i} + 3 \hat{j} - 5 \hat{k} \right) .\]
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Solution
The given line is parallel to the vector \[2 \hat{i} + 3 \hat{j} - 5 \hat{k} \] and the required line is parallel to the given line. So, the required line is parallel to the vector \[2 \hat{i} + 3 \hat{j} - 5 \hat{k} \] Hence, the equation of the required line passing through the point (2,-1, 3) and parallel to the vector \[2 \hat{i} + 3 \hat{j} - 5 \hat{k} \] is \[\overrightarrow{r} = \left( 2 \hat{i} - \hat{j} + 3 \hat{k} \right) + \lambda\left( 2 \hat{i} + 3 \hat{j} - 5 \hat{k} \right)\]
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