A PARTICLE MOVES WITH A SPEED OF 2 m/s IN THE DIRECTION OF THE VECTOR a=(5,-3,2) determine the x, y, and z components of the velocity vector

Find the maximum rate of change of f(x, y, z) = x+y/z at the point (1, -3, 5) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs:

Q1) (Vector Functions) It travels in a straight line to the point (4, 1, 4), has speed 2 at (1,2,3) and constant acceleration 3i –j+k. Find equation for the position vector r(t) of the particle at time t. At time t = 0, a particle is located at the point (1,2,3).

A velocity vector of v = 3t2i − 6t3 j − 4K ft/s is governing the movement of an object in the 3D space. If the object starts at (-1, 4, 5) at t = 0, determine the acceleration and position at t = 4s