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Date May Specimen paper Marks available 7 Reference code SPM.1.AHL.TZ0.8
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 0
Command term Find Question number 8 Adapted from N/A

Question

The plane П has the Cartesian equation 2x+y+2z=32x+y+2z=3

The line L has the vector equation r =(351)+μ(12p),μ,pR. The acute angle between the line L and the plane П is 30°.

Find the possible values of p.

Markscheme

recognition that the angle between the normal and the line is 60° (seen anywhere)       R1

attempt to use the formula for the scalar product       M1

cos 60° = |(212)(12p)|9×1+4+p2      A1

12=|2p|35+p2      A1

35+p2=4|p|

attempt to square both sides         M1

9(5+p2)=16p27p2=45

p=±357 (or equivalent)       A1A1

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » AHL 3.14—Vector equation of line
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Topic 3— Geometry and trigonometry

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