Question

Find parametric equations for the line through the point that is perpendicular to the given line, and intersects this line.
(0, 3, 1)
x = 3 + t, y = 3 - t, z = 4t
x = -55s
y = ?
z= ?

Answer 1

let P(0, 3, 1) and Q(3 + t,3 -t,4t)---> any point where the reqd line intersects the given line

Answer 2

now drs of PQ is 3+t,-t,4t-1
since PQ is perpendicular to the given line we have
(3+t)*1 +(-1)*(-t) +4(4t-1)=0

solving this we get the value of t and hence Q
our required line is PQ whose equation can be easily obtained

Answer 3

here t=1/18
hence
x=55s
y=3-s
z=1-14s