Question

Find the equation of the line which passes through the point P( 1,2,4) and is parallel to the line x = 2y = 3z.

Answer 1

x = 2y = 3z

x/1 = y/(1/2) = z/(1/3)
so a direction vector of the above line is <1, 1/2, 1/3> or < 6, 3, 2?

so the new line must pass through (1, 2, 4), so a possible equation would be
x = 1 + 6t
y = 2 + 3t
z = 4 + 3t

This is in parametric form. I am sure you can convert to other forms if needed.