Find the vector equation of the line passing through the point \( (1,2,-4) \) and perpendicular ...

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Find the vector equation of the line passing through the point \( (1,2,-4) \) and perpendicular to the two lines :
\[
\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7} \text { and } \frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5} .
\]
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