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Date November 2016 Marks available 4 Reference code 16N.1.AHL.TZ0.H_8
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number H_8 Adapted from N/A

Question

Consider the lines l 1 and l 2 defined by

l 1 :  r = ( 3 2 a ) + β ( 1 4 2 )  and l 2 : 6 x 3 = y 2 4 = 1 z where a is a constant.

Given that the lines l 1 and l 2 intersect at a point P,

find the value of a ;

[4]
a.

determine the coordinates of the point of intersection P.

[2]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

METHOD 1

l 1 : r  = ( 3 2 a ) = β ( 1 4 2 ) { x = 3 + β y = 2 + 4 β z = a + 2 β      M1

6 ( 3 + β ) 3 = ( 2 + 4 β ) 2 4 4 = 4 β 3 β = 3    M1A1

6 ( 3 + β ) 3 = 1 ( a + 2 β ) 2 = 5 a a = 7    A1

METHOD 2

{ 3 + β = 6 3 λ 2 + 4 β = 4 λ + 2 a + 2 β = 1 λ    M1

attempt to solve     M1

λ = 2 ,   β = 3    A1

a = 1 λ 2 β = 7    A1

[4 marks]

a.

OP = ( 3 2 7 ) + 3 ( 1 4 2 )    (M1)

= ( 0 10 1 )    A1

P ( 0 ,  10,  1 )

[2 marks]

b.

Examiners report

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

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.11—Vector equation of a line in 2d and 3d
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Topic 3—Geometry and trigonometry » AHL 3.12—Vector applications to kinematics
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