Just like the reaction of the weight of a body is a force acting on Earth towards the body, where and in what direction does the reaction of a gyroscopic force act?
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There is no "gyroscopic force". The best you can say is that there is a "reaction torque" when you apply a torque to a gyroscope. When a torque (which is a vector $\vec\Gamma$) is applied to a gyroscope with angular momentum (also a vector $\vec L$) the resulting motion of the gyroscope is a precession - the tip of the angular momentum vector rotates along the direction of the torque vector.
If you attempt to move a gyroscope such that its axis of rotation has to change, the reaction will be opposite to the direction of the torque you apply.
Floris
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i think the gyroscopic reaction torque is in the ratio of sine of angular momentum to the force applied. point to be noted that reaction force is less experienced when the gyro rotates at a lower rpm.>
nikhil swami
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