A displacement vector D has magnitude 50m and is directed 20∘ above the original x-axis. A new set of axes X′Y′ is obtained by rotating the original x- and y-axes anticlockwise through 30∘.
(a) Find the components of D along the new axes X′ and Y′.
(b) Reconstruct the vector D from the components obtained in part (a) and verify that its magnitude and original direction remain unchanged.