Verified answer

In Euclidian space a vector with three components F = (Fx,Fy,Fz) has "defined" magnitude

F = SqRt[Fx^2 + Fy^2 + Fz^2]

The usefullness of this definition is that the magnitude is an "invariant" (has the same value) regardless of the orientation of the (x,y,z) coordinate system.

In Special Relativity space & time coordinates mingle and it is useful to define a 4-vector with three space components and a fourth time component. G = (gt,gx,gy,gz).

The magnitude of a 4-vector is defined so that it is invariant when you measure it in different moving reference frames ala the Lorentz transformation of coordinates (ct,x,y,z).

This definition requires that the magnitude be defined as;

G = SqRt[gt^2,-gx^2,-gy^2,-gz^2)

When you apply this rule to your given 4-vector velocity y(c,vx,vy,vz) you should get the magnitude c.

EDIT______________________________________

I would add that the typical Euclidian 3-vector is also invariant, in magnitude, when viewed from frames of reference moving with constant velocity w.r/.t each other ,under so called Galliean transformations of coordinates. (non-relativistic).

To complete the analogy, the relativistic 4-vector is also invariant, in magnitude, when viewed from reference frames with different orientations.