Question

Given the equation of a line, [x, y, z] = [2, -1, -1] + k[1, 2, 4]

Determine the equation of line 3 through [1, 4 , -3] perpendicular to line 1.

Answer 1

No idea. What is line 1? 3?
To be ⊥, v1 • v2 = 0

Answer 2

all we need is a vector which is perpendicular to <1,2,4>
that is, their dot product is zero

One such vector is [-6,1,4]
So the equation could be [x,y,z] = (1,4,-3) + k[-6,1,4]
note that [-6,1,4] dot [1,2,4] = 0

There would be an infinite number of those lines.

I don't know what your reference to "line 3" is, was there more to this question?

Answer 3

@Reiny
Thanks for the help and yes there was another part but I got that already