Respuesta :
Answer:
[tex]\frac{x-2}{-1} =\frac{y-4}{1} =\frac{z-4}{-4} =t[/tex]
Step-by-step explanation:
Given that a line passes through P(2,4,4)
Also the line is perpendicular to the plane
[tex]-1x+1y-4z=1.[/tex]
From the equation of the plane we can say that normal to the plane has direction ratios as (-1,1,-4)
Since the required line is also perpendicular to the plane, the direction ratios of the required line is
(-1,1,4)
It passes through (2,4,4)
If Q(x,y,z) are general points on the line then
Direction ratios of PQ are = (x-2, y-4, z-4)
These are proportional to (-1,1,4)
So parametric form of the line is
[tex]\frac{x-2}{-1} =\frac{y-4}{1} =\frac{z-4}{-4} =t[/tex]
Whem t=0 we get the point P.
