The magnitude of the average velocity of a particle that moves from a point x = 3 cm, y = 10 cm and z = -4 cm to another point x=21 cm, y = 16 cm and z = 29 cm in time interval of 3 seconds is:

V_ave = (6, 2, 11) [cm/s]

Explanation:

To solve this problem we must remember the concept of average speed, which is equal to the space traveled within a given time interval. For this special case we have points on the three coordinate axes and the time that exists between the position changes in this way we identify the first point as A and the second point as B.

A (3, 10, -4) [cm]

B (21, 16, 29) [cm]

AB = (21, 16, 29) - (3, 10, -4)

AB = (18, 6, 33) [cm]

V_ave = 18/3 , 6/3, 33/3

Therefore the average speed in each component will be:

V_ave = (6, 2, 11) [cm/s]