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Date November Example questions Marks available 2 Reference code EXN.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 lines l1 and l2 have the following vector equations where λ,μ and m.

l1:r1=3-20+λ21m l2:r2=-1-4-2m+μ2-5-m

The plane Π has Cartesian equation x+4y-z=p where p.

 

Given that l1 and Π have no points in common, find

Show that l1 and l2 are never perpendicular to each other.

[3]
a.

the value of m.

[2]
b.i.

the condition on the value of p.

[2]
b.ii.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

attempts to calculate 21m·2-5-m        (M1)

=-1-m2        A1

since m20, -1-m2<0 for m         R1

so l1 and l2 are never perpendicular to each other        AG

 

[3 marks]

a.

(since l1 is parallel to Π, l1 is perpendicular to the normal of Π and so)

21m·14-1=0         R1

2+4-m=0

m=6        A1

 

[2 marks]

b.i.

since there are no points in common, 3,-2,0 does not lie in Π       

 

EITHER

substitutes 3,-2,0 into x+4y-zp        (M1)

 

OR

3-20·14-1p        (M1)

 

THEN

p-5        A1

 

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 3— Geometry and trigonometry » AHL 3.17—Vector equations of a plane
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Topic 3— Geometry and trigonometry

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