Question

find set of parametric equations for the line which passes through the point (3,4,7) that is perpendicular to the line with parametric equations x=1+t, y=3-t, and z=5t

Answer 1

That's almost identical to last problem

Answer 2

where did the 2,-1,-1 come from

Answer 3

from plugging in -1, -1 for b and c respectively

Answer 4

Dot product of two vector are zero if they are perpendicular
{1,-1,5}.{a,b,c}=0
a-b+5c=0
a=b-5c
This is vector for our line
{b-5c,b,c}

x=3+(b-5c)t
y=4+bt
z=7+ct