Line that intersects and is perpendicular to another line

[flame_m13]

Homework Statement

Find the line through (4, 1, -1) that intersects and is perpendicular to the line
{
x = -1 +t
y = -2 + t
z = 1 +t
}

Homework Equations

if they are perpendicular, the dot product of two vectors has to be zero.
The book gives me another hint, if (x, y, z) is the point of intersection, find it's coordinates.

The Attempt at a Solution

The direction vector for the line l is <1, 1, 1>
The vector for the line I'm trying to find is PQ = <(x-4), (y-1), (z+1)>
if i do the dot product, i get
(x-4)1 + (y-1)1 + (z+1)1 = 0.

at this point, the only x, y and z i can think of to make the whole thing zero are (4,1,-1)...

i am really confused on what i should do next.

 

[Dick]

Substitute the parametric form x=t-1 etc into the dot product equation. Find t.