The three vastus muscles are part of the quadriceps group. They are located at the front of the thigh and work to straighten the knee (or resist it being bent).
As well as working on the knee joint, these three muscles may act as tensioning devices for the muscles that pass over them, the long hip flexor muscles as well as other long hip muscles like gracilis, and the superficial portion of the gluteus maximus.
In addition the lateral and medial head can help in knee stabilization and controlling knee rotation.
The vastus lateralis, which is located to the outside of the thigh, attaches to the outer top corner of the knee cap. When activated, it may help to create an external rotation force on the lower leg relative to the femur.
The vastus medialis, which is the tear dropped shaped muscle attaching to the knee from the inner thigh, attaches to the top inner corner of the knee cap.
This muscle can be used to create an internal rotation force on the lower leg relative to the femur.
A portion of the vastus medialis called the vastus medialis obliquus attaches from the tendon of the adductor magnus long head and from there attaches to the knee cap. For this portion to activate, it needs a stable foundation. The adductor magnus long head needs to be activated.
When the adductor magnus long head is activated, it tends to rotate the thigh inwards. Acting against the gluteus maximus and other external rotators of the hip, it can act to help stabilize the femur against rotation. So, when it activates, it not only stabilizes the femur against rotation, which helps to anchor other knee rotators (popliteus and biceps femoris short head ), it also helps to anchor the vastus medialis obliquus, which also works to control knee rotation.
The vastus lateralis lies at the side of the thigh. The IT band runs over it from the hip crest to the tibia. Tension in the vastus lateralis can help take out the slack from the IT band making it easier for the either of the two muscles that attach to the top end of the IT Band to act on the tibia.
The tensor fascia latae attaches to the front edge of the IT band and when the vastus lateralis is engaged, the added tension in the It Band may make it easier for this muscle to act as a hip flexor.
Standing on one foot, tension in the vastus lateralis can remove slack from the IT band making it easier for both the tensor fascia latae and the superficial fibers of the gluteus maximus, which attach to the rear edge of the IT band to help stabilize the hip bone. This assumes that the shin is stabilized against rotation.
Assuming the hip bone is already stable, then these muscles could help to stabilize the tibia.
The rectus femoris is part of the quadriceps groups. It shares a common tendon with the three vastus muscles at the knee joint.
It runs over the vastus intermedius muscle.
Activation of the vastus intermedius muscle may help to remove slack from the rectus femoris, particularly when the hip joint is bent forwards (or "flexed") making it easier for the rectus femoris to act effectively in flexing the hip.
Vastus medialis forms the tear drop shape at the bottom of the inner thigh, just above the inside front corner of the knee.
One muscle that may be affected by vastus medialis activation (or lack of activation) is the sartorius. The sartorius attaches to the front point of the hip bone just above where the rectus femoris attaches.
Another is the gracilis. The gracilis attaches near the pubic bone.
Both muscles run down the inner thigh and cross the inside of the knee to attach to the tibia to form part of the pes anserinus or goose foot. The goose foot is attached to the shaft of the tibia just below the swelling of the knee.
As they run down the inside of the thigh, these two muscles (Sartorius and Gracilis) pass over the adductor muscles.
As mentioned, one of the adductor muscles, the long head of the adductor magnus, serves as an attachment point for a portion of the lower vastus medialis which is called the vastus medialis obliquus or VMO for short. And so activation of this adductor muscle in particular can help the vastus medialis obliquus activate which in turn may help to add tension to the sartorius and or gracilis making it easier for these muscles to activate effectively.
Activation of other adductors can also help to add tension to the sartorius and gracilis.
Note that as with the tensor fascia latae, when the knee is straight, or stabilized against changes in knee bent while actually bent, the sartorius can act as a hip flexor and so activation of the adductors and vastus medialis can help this muscle more effectively act as a hip flexor.
If the focus in on hip stability, say while standing on one leg, activation of all three vastus muscles and the adductors can help in stabilizing the knee and can add tension to overlying muscles making it easier to control the hip bone, or if the hip bone is stable, making it easier to stabilize the shin and foot.
In forward bends, it may be easier to actively flex the hips by activating the quadriceps. This isn't so much for reciprocal inhibition, but as a way of taking out the slack from the hip flexors to make it easier for them to actively bend the hips forwards.
I'd suggest here that reciprocal inhibition only comes into play with dynamic movements, not so much with static or slow moving actions.