Question

The equation of motion of a point in space is x = 2t, y = –4t, z = 4t where t measured in hour and the co-ordinates of moving point in kilometers. Find the distance of the point from the starting point O (0, 0, 0) in 10 hours.

Answer 1

Eliminating 't' from the given equations, we get the equation of the path as given point

Obviously, the path of the point is a straight line passing through origin (0, 0, 0)

When t = 10 hours the position of point is at x = 20, y = - 40, z = 40.

i.e., After 10 hours the position of point will be at (20, - 40, 40)

Therefore, required distance = distance between point (0, 0, 0) and (20, - 40, 40)