Page 07 MARKS 14. Two lines L1 and L2 are given by the equations: , , L x λ y λ z λ x y z L = + = + = − − − + = = − 1 2 4 3 2 4 7 3 8 1 1 3 2 : : (a) Show that the lines L1 and L2 intersect and find the point of intersection. (b) Calculate the obtuse angle between the lines L1 and L2. 15. Solve the differential equation 2 2 2 5 6 12 2 5 d y dy y x x dx dx + + = + − given y = -6 and 3 dy dx = , when x = 0. 16. A beaker of liquid was placed in a fridge. The rate of cooling is given by ( ), 0, F dT k T T k dt = − − > where TF is the constant temperature in the fridge and T is the temperature of the liquid at time t. • The constant temperature in the fridge is 4 °C. • When first placed in the fridge, the temperature of the liquid was 25 °C. • At 12 noon, the temperature of the liquid was 9·8 °C. • At 12:15 pm, the temperature of the liquid had dropped to 6·5 °C. At what time, to the nearest minute, was the liquid placed in the fridge? [END OF QUESTION PAPER] 5 4 10 9 Page 08 [BLANK PAGE] DO NOT WRITE ON THIS PAGE