Answer Happy

Kindly, the answers are needed to be solved step by step for abetter understanding, please!!
Question One (a) (i) Find the scalar product of u = <3, 5, 2> and v = <-1, 3, 0>. (ii) p = 10i-4i+7k and q = -2i+i+6k. Find p.q (b) Find the unit tangent vector of the following vector field. (i) r(t) = costi+sint j (ii) r(t) = (3£² + 2t)i + (2 − 4t³)j + (6t + 5)k (c) Find the tangent vector for (i) r(t) = e'i + 3ej+2e³tk (ii) (d) r(t) = 2 sin 2ti - 2 cos 2t - Evaluate the function f(3t² + 2t)i + (3t-6)i + (6t² + 5t² - 4)k dt. -1 and 3 2 - 2 sin sin (ii) (sin 2ti+tant j-e-2k)dt (c) Find a single vector which is perpendicular to the following vector. 213 at t=0 -3