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Date November 2016 Marks available 4 Reference code 16N.1.SL.TZ0.S_4
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number S_4 Adapted from N/A

Question

The position vectors of points P and Q are i  + 2 j   k and 7i  + 3j  4k respectively.

Find a vector equation of the line that passes through P and Q.

[4]
a.

The line through P and Q is perpendicular to the vector 2i +  nk. Find the value of n .

[3]
b.

Markscheme

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

valid attempt to find direction vector     (M1)

eg PQ ,   QP

correct direction vector (or multiple of)     (A1)

eg 6i  +  j   3k

any correct equation in the form r  =  a  +  tb (any parameter for t )     A2     N3

where a is i  +  2j   k or 7i  +  3j   4k , and b is a scalar multiple of 6i  +  j   3k

eg r  =  7i  +  3j   4k  +  t(6i  +  j   3k), r  = ( 1 + 6 s 2 + 1 s 1 3 s ) ,   r = ( 1 2 1 ) + t ( 6 1 3 )

 

Notes: Award A1 for the form a  +  tb, A1 for the form L  =  a  +  tb, A0 for the form r  =  b  +  ta.

 

[4 marks]

a.

correct expression for scalar product     (A1)

eg 6 × 2 + 1 × 0 + ( 3 ) × n ,   3 n + 12

setting scalar product equal to zero (seen anywhere)     (M1)

eg u   v  = 0 ,   3 n + 12 = 0

n = 4    A1     N2

[3 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 3.13—Scalar and vector products
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