8 In the diagram to the right, AD and BE are altitudes of AABC intersecting at P. Let a, b, c and p be the respective position vectors of A, B, C and P relative to an origin O. a Explain why (pa) (c- b) = 0. b Explain why (pb) (ac) = 0. c Hence show that (pc) (a - b) = 0. d Deduce that the three altitudes of a triangle are concurrent. A EQ P D B

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