Mathematics (AS & A Level) · Oct / Nov 2018 · Paper 13 · Question 6
9709
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O A B C D E F G 8 6 7 4 2 i j k The diagram shows a solid figure OABCDEFG with a horizontal rectangular base OABC in which OA = 8 units and AB = 6 units. The rectangle DEFG lies in a horizontal plane and is such that D is 7 units vertically above O and DE is parallel to OA. The sides DE and DG have lengths 4 units and 2 units respectively. Unit vectors i, j and k are parallel to OA, OC and OD respectively. Use a scalar product to find angle OBF, giving your answer in the form cos−1 0a b 1 , where a and b are integers. [6] 9
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