A-LevelFurther MathematicsVectors9231/12 · May/June 2017 · Q1314 Marks

The position vectors of the points A, B, C, D are i+j+3k, 3i – j + 5k, i − j + k, 5i – 5j + αk, respectively, where α is a positive integer. It is given that the shortest distance between the line AB and the line CD is equal to 2√2.

(i)Show that the possible values of α are 3 and 5.[7]
(ii)Using α = 3, find the shortest distance of the point D from the line AC, giving your answer correct to 3 significant figures.[3]
(iii)Using α = 3, find the acute angle between the planes ABC and ABD, giving your answer in degrees.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

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Topic: Vectors, A-Level Further Mathematics (syllabus 9231). Structured question, 14 marks.
Source: A-Level Further Mathematics, May/June 2017 Paper 1 Variant 2, question 13.

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