- [Maximum mark: 7]
A duck is sitting in a duck pond at point A(7, 4, 0) relative to an origin O, where lengths are measured in metres and time, t, is measured in seconds. It takes off and flies in a straight line with vector equation
d = (7, 4, 0) + t(6, 6, 3).
(a) Find the speed of the duck through the air (in ms⁻¹). [2]
A hawk hovering at position vector (−38, 134, 315), relative to O, sees the duck take off and immediately dives from its position with constant velocity vector (15, −20, −60) to intercept the duck.
(b) Write down the vector equation for h, that models the flight of the hawk. [1]
(c) Find the position vector at which the hawk intercepts the duck. [4]