User interface language: English | Español

Date November 2020 Marks available 2 Reference code 20N.1.SL.TZ0.S_9
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Express Question number S_9 Adapted from N/A

Question

Points A and B have coordinates 1, 1, 2 and 9, m, -6 respectively.

The line L, which passes through B, has equation r=-3-1924+s24-5.

Express AB in terms of m.

[2]
a.

Find the value of m.

[5]
b.

Consider a unit vector u, such that u=pi-23j+13k, where p>0.

Point C is such that BC=9u.

Find the coordinates of C.

[8]
c.

Markscheme

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

valid approach to find AB        (M1)

eg     OB-OA , A-B

AB=8m-1-8       A1     N2

[2 marks]

a.

valid approach        (M1)

eg     L=9m-6 , 9m-6=-3-1924+s24-5

one correct equation        (A1)

eg       -3+2s=9, -6=24-5s

correct value for s            A1

eg       s=6

substituting their s value into their expression/equation to find m       (M1)

eg       -19+6×4

m=5       A1     N3

[5 marks]

b.

valid approach        (M1)

eg     BC=9p-63, C=9u+B , BC=x-9y-5z+6

correct working to find C        (A1)

eg     OC=9p+9-1-3, C=9p-2313+95-6, y=-1 and z=-3

correct approach to find u (seen anywhere)            A1

eg     p2+-232+132 , p2+49+19

recognizing unit vector has magnitude of 1        (M1)

eg     u=1 , p2+-232+132=1 , p2+59=1

correct working        (A1)

eg     p2=49 , p=±23

p=23            A1

substituting their value of p        (M1)

eg     x-9y-5z+6=6-63, C=6-63+95-6, C=923-2313+95-6, x-9=6

C15, -1, -3  (accept 15-1-3)     A1     N4

 

Note: The marks for finding p are independent of the first two marks.
For example, it is possible to award marks such as (M0)(A0)A1(M1)(A1)A1 (M0)A0 or (M0)(A0)A1(M1)(A0)A0 (M1)A0.

 

[8 marks]

c.

Examiners report

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

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.10—Vector definitions
Topic 3—Geometry and trigonometry » AHL 3.11—Vector equation of a line in 2d and 3d
Topic 3—Geometry and trigonometry

View options