16 6. A mining company has identified a mineral layer below ground. The mining company wishes to drill down to reach the mineral layer and models the situation as follows. With respect to a fixed origin O,  the ground is modelled as a horizontal plane with equation z = 0  the mineral layer is modelled as part of the plane containing the points A(10, 5, –50), B(15, 30, –45) and C(–5, 20, –60), where the units are in metres (a) Determine an equation for the plane containing A, B and C, giving your answer in the form r . n = d (5) (b) Determine, according to the model, the acute angle between the ground and the plane containing the mineral layer. Give your answer to the nearest degree. (3) The mining company plans to drill vertically downwards from the point (5, 12, 0) on the ground to reach the mineral layer. (c) Using the model, determine, in metres to 1 decimal place, the distance the mining company will need to drill in order to reach the mineral layer. (2) (d) State a limitation of the assumption that the mineral layer can be modelled as a plane. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________