Define angular momentum `(vec(L))` and torque `(vec(tau))` Show that `(d vec(L))/(dt) = vec(tau)`.

Define angular momentum ( vecL ) and torque ( vecr ). Show that (dvecL)/dt = tau .

For any two vectors vec(a) and vec(b) , show that | vec (a).vec(b)| le |vec(a)||vec(b)|

ABCD is a parallelogram. If L and M be the middle points of BC and CD, respectively express vec(AL) and vec(AM) in terms of vec(AB) and vec(AD) . Also show that vec(AL)+vec(AM)=(3//2)vec(AC) .

Show that the angular momentum of a particle under the action of the force vec(F) = k vec(r ) is conserved , where K is a constant quantity.

For the vectors vec(a) " and " vec(b) show that (i) abs(vec(a)+vec(b)) le abs(vec(a))+abs(vec(b)) " (ii) " abs(abs(vec(a))-abs(vec(b))) le abs(vec(a)-vec(b))

If vec(a) + vec(b) + vec (c ) = vec(0) , show that vec(a) xx vec(b) = vec(b) xx vec(c ) = vec(c ) xx vec(a)

If vec(alpha) and vec (beta) are perpendicular to each other , show that | vec(alpha) + vec(beta)|^(2) = |vec(alpha)-vec(beta)|^(2)

If vec(a)=vec(OA) " and " vec(b)=vec(AB), " then " vec(a)+vec(b) is -

A rectangular loop of size lxxb carrying a steady current I is placed in a uniform magnetic field vec(B) . Prove that the torque vec(tau) acting on the loop is given by vec(tau)=vec(m)xxvec(B) , "when " vec(m) is the magnetic moment of the loop .

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular