In this question i\mathbf{i}i and j\mathbf{j}j are perpendicular unit vectors representing due east and due north respectively.
A surveillance drone, DDD, is flying along a triangular path ABCABCABC at a constant speed.
The drone moves around the triangle in an anticlockwise direction, starting its circuit from vertex AAA.
On the leg from AAA to BBB, the velocity vector of the drone is (2i+23j) m s−1(2\mathbf{i} + 2\sqrt{3}\mathbf{j})\text{ m s}^{-1}(2i+23j) m s−1.
Find the speed of the drone as it moves from AAA to BBB.
On the leg from BBB to CCC, the velocity vector of the drone is −4i m s−1-4\mathbf{i}\text{ m s}^{-1}−4i m s−1. Show that the interior angle ABC=60∘ABC = 60^\circABC=60∘.
The triangular path ABCABCABC is equilateral. The drone completes one full circuit and returns to its starting position at AAA after exactly 18 seconds.
Vertex BBB lies at position vector [−35]\begin{bmatrix} -3 \\ 5 \end{bmatrix}[−35] metres with respect to a fixed origin OOO.
Find the position vector of vertex CCC.
