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Date November 2017 Marks available 4 Reference code 17N.2.sl.TZ0.3
Level SL only Paper 2 Time zone TZ0
Command term Find Question number 3 Adapted from N/A

Question

Let \(\overrightarrow {{\text{AB}}} = \left( {\begin{array}{*{20}{c}} 4 \\ 1 \\ 2 \end{array}} \right)\).

Find \(\left| {\overrightarrow {{\text{AB}}} } \right|\).

[2]
a.

Let \(\overrightarrow {{\text{AC}}} = \left( {\begin{array}{*{20}{c}} 3 \\ 0 \\ 0 \end{array}} \right)\). Find \({\rm{B\hat AC}}\).

[4]
b.

Markscheme

correct substitution     (A1)

eg\(\,\,\,\,\,\)\(\sqrt {{4^2} + {1^2} + {2^2}} \)

4.58257

\(\left| {\overrightarrow {{\text{AB}}} } \right| = \sqrt {21} \) (exact), 4.58     A1     N2

[2 marks]

a.

finding scalar product and \(\left| {\overrightarrow {{\text{AC}}} } \right|\)     (A1)(A1)

scalar product \( = (4 \times 3) + (1 \times 0) + (2 \times 0){\text{ }}( = 12)\)

\(\left| {\overrightarrow {{\text{AC}}} } \right| = \sqrt {{3^2} + 0 + 0} {\text{ }}( = 3)\)

substituting their values into cosine formula     (M1)

eg cos B\(\hat A\)C\({\text{ = }}\frac{{4 \times 3 + 0 + 0}}{{\sqrt {{3^2}}  \times \sqrt {21} }},{\text{ }}\frac{4}{{\sqrt {21} }},{\text{ }}\cos \theta  = 0.873\)

0.509739 (29.2059°)

\({\rm{B\hat AC}} = 0.510\) (29.2°)     A1     N2

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 4 - Vectors » 4.2 » The angle between two vectors.
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