Finding the parametric and vector forms of the line is perpendicular to lines $(4t,1+2t,3t)$ and $(−1+s,−7+2s,−12+3s)$
And passes through the point of the intersection of two lines
A vector perpendicular to these lines is $$v = (4, 2, 3) \times (1, 2, 3) = [0, -9, 6]$$
How would I write the vector / parametric form?
HINT
We have found the direction vector $\vec v$ for the perpendicular line, now we need the intersection point $P_0$ to determine the parametric equation
$$P(t)=P_0+t\vec v$$