I take the position that Accelerator cannot control the magnitude of vectors.
Indirect textual evidence
The Japanese for Accelerator's "vector manipulation" ability is: 向き【ベクトル】変換. The two fundamental properties of a vector are magnitude (大きさ) and direction (向き). If we ignore the furigana on 向き, Accelerator's ability translates as "direction changing" or "direction transformation". (Also, 向き isn't a synonym for vector in any standard usage, so there's clearly an emphasis on the "direction" aspect here.)
Consider the following quote from volume 15, with all furigana preserved:
Roughly translated, this comes out to:
Accelerator brought together some manner of vectors (ベクトル), altered their direction (向き), brought them to a point, and attacked Kakine Teitoku.
We see here that there is an explicit reference to modifying the direction of vectors, and no reference to modifying the magnitude of vectors. This doesn't prove anything directly, but its absence is reasonably informative.
A cursory search across all 22 volumes of the initial light novel series (i.e. before New Testament) plus the two associated side story volumes reveals no cases in which 大きさ was mentioned within a few lines of ベクトル. (I might've missed something, though; this isn't all that great evidence. I'm just pointing out that there seem to be no references to the matter of magnitude either way.)
Direct physical evidence that Accelerator cannot control vector magnitudes cannot exist (you can't prove a negative). It is easy, however, to demonstrate a reasonably plausible physical mechanism by means of which Accelerator could do everything he does without needing to control the magnitude of vectors (as I will do below). By the principle of parsimony, it follows that we need not assume that Accelerator is able to control vector magnitudes.
We begin by looking at energetic considerations. Consider a 1 kg lump of iron that is at room temperature. Roughly speaking, the total thermal energy of that lump is on the order of 1e5 ~ 1e6 joules. This is sufficient energy to propel a 50 kg human at a velocity of ~100 mi/hr, or a 50 g stone at ~3000 mi/hr (~Mach 4). If Accelerator is in contact with the earth, he has access to an energy reservoir roughly 1e24 times larger. Conclusion: Accelerator has access to enough energy to do pretty much anything, if he has a way to harness some or all of the thermal energy of objects he is in contact with.
The question remains: can Accelerator harness thermal energy? I claim the answer is yes.
Let us assume for the sake of argument that the only thing Accelerator can do is take a moving particle and alter its direction of motion (we're going to handwave our way past things like wavefunctions, Heisenberg uncertainty, and [in particular] conservation of momentum, because obviously Accelerator couldn't exist in the real world, so some physical laws have to give). Using this framework, let's see how Accelerator can do some things.
- Accelerator wants to launch a stone at supersonic speeds. To do so, he directs the momentum vectors of a suitably-sized portion of the earth in the direction he wants the rock to move. This portion of the earth mostly-elastically collides with the stone and transfers its momentum to the stone, launching the stone at high speed. The aforementioned portion of earth gets slightly colder, but the earth is a huge heat reservoir, so it doesn't really make a difference.
- Accelerator wants to launch himself at Touma. He uses his ability to direct the momentum vectors of a suitably-sized portion of the earth in the direction he wants. Elastic collisions happen, and he goes flying at Touma. If the momentum of the portion of the earth he's manipulating isn't large enough to get him moving fast enough after an elastic collision, he can augment the momentum of that portion by having the surrounding portions of the earth elastically transfer momentum into that portion, repeating as necessary to get the part that will collide with him moving fast enough. Elastic collisions in solids happen pretty quickly, so this should give him good reaction time.
In general, I don't think it's possible to formulate a valid argument of the form "Accelerator is capable of doing X, therefore he must be able to manipulate vector magnitudes". As long as Accelerator has access to warm matter (which he does unless you stick him in a vacuum), he has access to particles in motion, with their associated momentum vectors, which can be manipulated to do just about anything.
Take all of this with a grain of salt - as the perennial "can Flash beat Accelerator" debates (and their ilk) demonstrate, Accelerator's abilities are not well-defined in a physical sense. Vectors don't physically exist - they're merely a useful mathematical abstraction we use to describe certain features of the universe. Trying too hard to justify Accelerator's abilities in terms of physical principles is a recipe for failure. In the end, Accelerator's vector manipulation does whatever Kamachi wants it to do.