Turn over 11 Question 3 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 3 is 8 marks) 12 4. n vA vL Figure 2 A small aircraft is landing in a field. In a model for the landing the aircraft travels in different straight lines before and after it lands, as shown in Figure 2. The vector vA is in the direction of travel of the aircraft as it approaches the field. The vector vL is in the direction of travel of the aircraft after it lands. With respect to a fixed origin, the field is modelled as the plane with equation x – 2y + 25z = 0 and vA = 3 2 1 − −         (a) Write down a vector n that is a normal vector to the field. (1) (b) Show that n × vA = λ 13 19 1        , where λ is a constant to be determined. (2) When the aircraft lands it remains in contact with the field and travels in the direction vL The vector vL is in the same plane as both vA and n as shown in Figure 2. (c) Determine a vector which has the same direction as  vL (3) (d) State a limitation of the model. (1) _____________________________________________________________________________________ _____________________________________________________________________________________