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 x-axis 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|= (0i-2j+k)/5

(ii) is a plane, thus a unit vector that is normal to the plane is v/|v|= (3i-4j+k)/26

is my answer is correct??? pls help me... tq