MATH1510 Lecture : Maths assignment-3

Please show all the steps!!! Thanks!! 1) Which of the following vector-valued functions parameterize the same pace curve? Explain your answer. (a) (-2+cosi)i+9j+(3-sin t)k (b) (2+cos t)i-9j+(-3-sin t)k (c) (-2+cos3t)i+9j+(3-sin3t)k (d) (-2-cos t)i+9j+(3+sin t)k (e) (2+cos t)i+9j+(3+sin t)k

Given the acceleration vector A(t) = t2 i - 2 j + e3t k, and the initial position R(0) = 2i+j - k and velocity V(0)= i - j - 2 k, find (A) the velocity and (B) the position vector at time t. V(t) = i + j + k R(t) = i + j + k

Given that the acceleration vector is a (t) = (-4 cos(-2t)) i + (-4 sin (-2t)) j + (-4t)k, the initial velocity is v (0) = i + k, and the initial position vector is r (0) = i + j + k, compute: The velocity vector v (t) = i+ j+ k The position vector r (t) = i+ j+ k