
vector in space
Question :
describe the set of points in space whose coordinate satisfy the given equation or pair of equations:
(i) z=2y (ii) 3x=4y, z=1
if (i) or (ii) represents a line in space, give a unit vector that is parallel to the line. If (i) or (ii) represents a plane, give a unit vector that is normal to the plane.
My attempt :
z=2y is a line parallel to xaxis consisting of all points of the form (0,z,z)
3x=4y, z=1 is a plane perpendicular to the z=1 axis consisting of all points of the form (3x,3x,1)
(i) is a line, thus the unit vector that is parallel to the line is v/v= (0i2j+k)/5
(ii) is a plane, thus a unit vector that is normal to the plane is v/v= (3i4j+k)/26
is my answer is correct??? pls help me... tq

I'm afraid you're a bit off. A location in 3dimensional space must be described by three variables. But a position on a line requires only one variable. A position on a plane requires two variables. So, if you're talking about a line, how many equations must you have in order to knock down the number of variables from 3 to 1? If you're talking about a plane, how many equations must you have in order to knock down the number of variables from 3 to 2?

I am no expert as Ackbeet.
I believe (1) is a plane because
(2) is a line because z=1 and
