The position of Pioneer 11 is between Voyager 1 and 2, that means Pioneer 11 is closer to Voyager 1 and 2 than to Earth.
According to the Wikipedia article on Pioneer 11 we lost communication with it on November 30, 1995.
Is there any way to communicate with Pioneer 11 through Voyager 1 or 2 ?
The fundamental problems that prevent this are:
Pioneers 10 and 11 both have shut down due to insufficient power to operate both the computer and the radio at the same time.
NASA uses huge antennae to capture the weak signals from the probes. The smallest dishes used are around 10m across, and in recent years, they've been using the larger (around 30m) dishes.
The Pioneer probes, in order to make this work, would have to be "effectively closer" to the Voyagers than to Earth, be able to power up, and be able to aim at the Voyager probe being used.
This means the Pioneer would need to receive, process, and obey instructions to point at the Voyager, and the only way such a relay would be known would be after it worked. But this would require that we be able to send those instructions in the first place, and if it's operational at all, it's aimed at Earth.
But further, it's not just the Pioneer that would need to point... the Voyager would have to aim at the Pioneer to make it work. And that means it would not be aimed at Earth. See #5...
Radio follows an inverse square law. In order to pick up the 8w signal from 36 AU, NASA needed the 36m antenna on the ground. Voyager's antenna is under 3m.
Pioneer 11 for Thu 13 February 2014 Right Ascension: 18h 49m 45.2s Declination: -8° 48' 07.3" (J2000) Sun dist: 13,202,867,763 km [11.4 km/s] Earth dist: 13,319,310,346 km [27.4 km/s] Constellation: Sct Magnitude: N.A.
Voyager 1 Spacecraft, ephemeris for Thu 13 February 2014, 00:00 UTC Right Ascension: 17h 11m 59s Declination: +12° 02’ 31” (J2000) [HMS|00:00:00|Dec] Distance from Sun: 18,977.42 Million Km Distance from Earth: 19,021.59 Million Km Magnitude: N.A. Constellation: Oph
Voyager 2 Spacecraft, ephemeris for Thu 13 February 2014, 00:00 UTC Right Ascension: 20h 00m 25s Declination: -55° 57’ 34” (J2000) [HMS|00:00:00|Dec] Distance from Sun: 15,563.42 Million Km Distance from Earth: 15,663.78 Million Km Magnitude: N.A. Constellation: Tel
This gives us a minimum of 20° difference in angle, and the distances can be roughly calculated based upon a 100AU triangle... Given 100 x Sin(20°) that's 34 AU and change. Voyager's dish isn't big enough, at 3.6m; it pulls in roughly 1/100 the signal that the 36m dish on earth would. (other factors make this extremely simplistic an analysis, but establish the point well enough.)
Simply put, the receiver is not sensitive enough, and the antenna gain not sufficient, to enable voyager to notice the energy from a pioneer transmitter.
Voyager probes don't have a whole lot of memory. And much of that memory is of dubious reliability now. The reprogramming would need to revise the whole mission programming, even if Voyager could "hear" the Pioneer 11 transmission.
This would scrap ongoing data collection, possibly cripple the Voyager, and still not assure that the data would relay.
Given that any one of the five reasons is sufficient for a no-go on such an attempt, it's a fairly certain thing that no space probe is going to be used to contact the Pioneers.
Whether a later probe might be used to relay to/from the Voyagers is another matter.
No, absolutely none. Even assuming Pioneer 11's transceiver still works, and there's no reason to believe that, that image you attach of distances between the three probes isn't showing it proportionally correct, since it's merely an approximate slice of euclidean space and is not axially aligned with anything to correctly appreciate distances involved. So here's NASA's own depiction of relative positions of the mentioned space probes that should provide a better view:
Relative Positions of Distant Spacecraft
This graphic shows the relative positions of NASA’s most distant spacecraft in early 2011, looking at the solar system from the side. Voyager 1 is the most distant spacecraft, about 17.5 billion kilometers (10.9 billion miles) away from the sun at a northward angle. Pioneer 10, the next most distant, is about 15.4 billion kilometers (9.6 billion miles) away from the sun on the opposite side of the solar system. Voyager 2 is about 14.2 billion kilometers (8.8 billion miles) away from the sun on a southward trajectory, on the same side of the solar system as Voyager 1. Pioneer 11 is about 12.4 billion kilometers (7.8 billion miles) away from the sun. New Horizons is about 3 billion kilometers (2 billion miles) away from the sun, on its way to Pluto.
Image and quote source: NASA
As you see from the right hand side part of the image, the three probes are all moving in direction away from the Sun at different inclinations to the ecliptic, for example Pioneer 11 at 17° and Voyager 2 at 79° relative to the ecliptic plane of the Solar system. To calculate their relative distances between each other, we'd have to first calculate their absolute positions, their cartesian coordinates $x, y, z$ in three dimensions, and then use formula to calculate their relative distances in 3-dimensional space:
$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$$
Now, I don't have exact numbers and extracting them from other equations would take too long, so let's just take rough approximations from the NASA's image, and make this dimensionless calculation. We can probably agree that both Voyager 1 and Voyager 2 are at least 0.7 units away from Pioneer 11 on our $y$ axis (let's say that $x, y$ are depicted on the right part of the image, and $x, z$ on the left part of it), that Pioneer 11 is 1 unit away from the Sun on the $x$ axis, putting Voyager 2 at about the same distance, while Voyager 1 is perhaps 1.1 units away. And on our $z$ axis, let's say that Pioneer 11 and Voyager 2 are separated by 0.5 of our relative, dimensionless units. OK, let's plug these numbers in our calculator. For distance between Pioneer 11 and Voyager 2 that seem to be the closest to each other, we get:
$$\sqrt{(1 - 1)^2 + (-0.7 - 0.2)^2 + (1.5 - 1)^2}$$
Or roughly 1.03 of our units, where we said that 1 of these units is the distance between Pioneer 11 and the Sun. This means that Pioneer 11 and Voyager 2 are at roughly the same distance to each other as Pioneer 11 is to the Earth. So this necessarily means that communication between the probes wouldn't be possible even if one of the two probes involved carried the Arecibo antenna and the power required for it with it. Clearly, none of them do, so the answer to your question is a resounding no.
No. And here's why:
To establish radio communication between two points in space successfully, one has to achieve the Signal-to-Noise ratio (SNR) greater than some threshold which varies depending on the type of signal modulation and error correction used.
This is done through several means:
The Pioneers were equipped with three antennas, but the tradeoff here is obvious: accuracy vs. antenna gain.
To achieve precise pointing you have to know exactly where the other end of the link will be by the time your signal gets there. After losing comms with P-11, the position uncertainty has grown large.
The Voyagers are very limited in their ability to point precisely in a given direction, and by changing their attitude to hunt for the Pioneer you risk losing the chance to re-establish Voyagers' own link to the Earth.
Usually, to compensate for sub-optimal antenna positioning, you increase the power output through the transmitter. Unfortunately, Voyagers don't have much power available now. This power is abundant here on Earth, so Deep Space Network can pour megawatts into space through large-gain parabolic dishes with very fine servo-mechanisms.
You can lower noise in the receiver. Shutting off sources of interference, lowering the temperature of receiver components (to get rid of extra thermal noise) may help, but this is not really feasible for a spacecraft which doesn't know when to do that. DSN transceivers, again, are much better in this regard.
You can lower the SNR threshold by accumulating and processing more of the incoming signal (that is, you lower the communication bitrate) and improving the processing algorithms. A spacecraft flying on its own deep in space has no ability to download better code.
While the main question can be confidently answered negatively, the idea of relaying data through other spacecraft is currently in wide use - e.g., in Mars rovers. Certainly, here the main enabling factor is much lower distance between the rover and the Mars-orbiting craft.
