2 A plane is flying on a course of 060° in still air at a speed of 300 km hr-', when it passes a control tower, A. Using i and j as the unit vectors due east and due north respectively, express the position vector of the plane relative to the control tower in terms of t, the time in hours since passing A. The next control at which the plane must report, B, has a position 300/3i + 150j relative to Show that, after 90 minutes of travel, the plane is 150 km away from B. b Find the length of time that the plane is less than 150 km from B.

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