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Tutorial questions - Vector differentiation 1. A particle moves along the curve with displacement vector r = (2+2, t2 – 4t, 3t - 5) a time t. (a) Find the velocity and acceleration vectors of the particle at any time t. (b) Find the components, in the direction of the vector (1, -3,2), of the velocity and acceleration vectors at time t = 2. (Hint: the component of a vector a in the direction of a vector b is the number (al cos , where o is the angle between a and b. (c) Find the components, in the direction tangential to the path of the particle, of th velocity and acceleration vectors at time t = 1. 2. If u = (t2, t, 1) and v= (Int, et, t), verify the rules for differentiation for d (u. v) an (u x v) by evaluating each side separately. 3. For a plane curve with polar equation r =r(e), note that r=r(O)(cos 6, sin 6). Use th dt