Two drones, Alpha and Beta, travel along straight-line paths in a horizontal surveying area.
Drone Alpha maintains a constant velocity of (9i+12j) m s−1(9\mathbf{i} + 12\mathbf{j}) \text{ m s}^{-1}(9i+12j) m s−1.
Drone Beta travels from the position vector (−5i+10j)(-5\mathbf{i} + 10\mathbf{j})(−5i+10j) metres to the position vector (22i+46j)(22\mathbf{i} + 46\mathbf{j})(22i+46j) metres over a duration of 6 seconds.
Show that the direction of motion of Beta is parallel to the direction of motion of Alpha.
A technician suggests that Beta must be moving with a constant velocity of (4.5i+6j) m s−1(4.5\mathbf{i} + 6\mathbf{j}) \text{ m s}^{-1}(4.5i+6j) m s−1. Explain why this statement might be false.
A third drone, Gamma, flies at a constant speed of 10 m s−110 \text{ m s}^{-1}10 m s−1 along a separate straight path. The flight paths of Alpha and Gamma intersect at a fixed waypoint XXX.
It is recorded that:
Demonstrate that the flight paths of Alpha and Gamma are perpendicular.
