Find the vector equation of a line passing through the point with position vector ` hat i-2 hat j-3 hat k` and parallel to the line joining the points with position vectors ` hat i- hat j+4 hat ka n d2 hat i+ hat j+2 hat kdot` Also, find the Cartesian equivalent of this equation.

Explanation

Since vector equation of a line passing through a vector `bar{a}` and its parallel vector `bar{b}` is


`
overline{{r}}=overline{{a}}+{t} overline{{b}}`



line passing through the vector `2 hat{i}-hat{j}+hat{k} `and its parallel vector is

`

hat{i}+2 hat{j}+hat{k}-(-hat{i}+4 hat{j}+hat{k})`

`

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