Originally Posted by

**samantha_malone** in this question, distance is in kilometers, time is in hours.

a balloon is moving at a constant height with a speed of 18kmh^-1, in the direction of the vector (3,4,0)

At time t = 0, the balloon is at point B with coordinates (0,0,5).

(a) Show that the position vector b of the baloon at time t is given by b = (x,y,z) = (0,0,5) + t(10.8, 14.4, 0)

At time t = 0, a helicopter goes to deliver a message to the baloon. The position bector h of the helicopter at time t is given by h = (x,y,z) = (49, 32, 0) + t(-48, -24, 6).

(b) (i) Write down the coordinates of the starting position of the helicopter.

(ii) find the speed of the helicopter.

(c) the helicopter reaches the baloon at point R.

(i) Find the time the helicopter takes to reach the baloon.

(ii) Find the coordinates of R.

Thanks!