Find the vector equation of a line passing through the point with position vector \( (2 \hat{i}-...

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Find the vector equation of a line passing through the point with position vector \( (2 \hat{i}-3 \hat{j}-5 \hat{k}) \) and perpendicular to the plane \( \vec{r} \cdot(6 \hat{i}-3 \hat{j}-5 \hat{k})+2=0 \). Also, find the point of intersection of this line and the plane.
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