optics of moving sources

the question is .Apoint object is moving with a speed v before an arrangement of two mirrors as shown in figure. Find the velocity of image in mirror M₁ with respect to image in mirror M₂

For V_m1:
Take a unit vector along the mirror m₁ and one perpedicular to m₁

Now component of velocities along the mirror will be same and same but opposite sign perpendicular to the mirror

It can be easily determined to be
V_m1=v(cos 2θ i +sin 2θ j)
and V_m2=v i

hence,
V_m1/m2=V_m1-V_m2