Question

Consider the line in 3-space through the point (4, -2, -2) that is parallel to the vector (7, 5, -2). Find a point of other than (4, -2, -2) that lies on the line.

Answer 1

I got the vector equation of the line as (x-3, y+5, z+2)=t(7, 5, -2)

Answer 2

a line has a slope (vector) that can be scaled t<Vx,Vy,Vz>

and its anchored to a point (Px,Py,Pz)

x = Px +t Vx
y = Py +t Vy
z = Pz +t Vz

change the value of t to find all points on the line