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1.If a particle with mass m moves with position vector r(t), then its angular momentum is defined as and its torque as L(t) = mr(t) x v(t) and its torque as t(t) = mr(t) x a(t). Show that L'(t) = t(t). Deduce that if t(t) = 0 for all t, then L(t) is constant. (This is the law of conservation of angular momentum.) 2. Find the limit of Lim too '2+3-1' 3. Find the vector equation and parametric equation for the line segment that joints P to Q P(2,0,0) , Q(6,2,-2) 4. Find the vector function that represents the curve of intersection of the two surfaces x2+2=4 and the surface z = Xy 5.find the derivative of the vector function r(t) = sin at i+ tebtj + cos2ct k 6. Find the unit tangent vector T(t) at the point with the given value of the parameter t r(t) = sin't i + cost j + tant k, t = pi/4 7. Find the parametric equations for the tangent line to the curve with the given parametric equations at the specified point x=In(t+1), y=t cos2t, z=2t , (0,0,1)