User interface language: English | Español

Date May 2019 Marks available 1 Reference code 19M.1.AHL.TZ2.H_2
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number H_2 Adapted from N/A

Question

Three points in three-dimensional space have coordinates A(0, 0, 2), B(0, 2, 0) and C(3, 1, 0).

Find the vector  AB .

[1]
a.i.

Find the vector  AC .

[1]
a.ii.

Hence or otherwise, find the area of the triangle ABC.

[4]
b.

Markscheme

AB = ( 0 2 2 )       A1

Note: Accept row vectors or equivalent.

[1 mark]

a.i.

AC = ( 3 1 2 )       A1

Note: Accept row vectors or equivalent.

[1 mark]

a.ii.

METHOD 1

attempt at vector product using  AB and  AC .      (M1)

±(2i + 6j +6k)      A1

attempt to use area  = 1 2 | AB × AC |        M1

= 76 2 ( = 19 )       A1

 

METHOD 2

attempt to use  AB AC = | AB | | AC | cos θ        M1

( 0 2 2 ) ( 3 1 2 ) = 0 2 + 2 2 + ( 2 ) 2 3 2 + 1 2 + ( 2 ) 2 cos θ

6 = 8 14 cos θ       A1

cos θ = 6 8 14 = 6 112

attempt to use area  = 1 2 | AB × AC | sin θ        M1

= 1 2 8 14 1 36 112 ( = 1 2 8 14 76 112 )

= 76 2 ( = 19 )       A1

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 3— Geometry and trigonometry » AHL 3.12—Vector definitions
Show 77 related questions
Topic 3— Geometry and trigonometry » AHL 3.16—Vector product
Topic 3— Geometry and trigonometry

View options