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Date May 2015 Marks available 5 Reference code 15M.2.sl.TZ2.2
Level SL only Paper 2 Time zone TZ2
Command term Find Question number 2 Adapted from N/A

Question

Let \(u = 6i + 3j + 6k\) and \(v = 2i + 2j + k\).

Find

(i)     \(u \bullet v\);

(ii)     \(\left| {{u}} \right|\);

(iii)     \(\left| {{v}} \right|\).

[5]
a.

Find the angle between \({{u}}\) and \({{v}}\).

[2]
b.

Markscheme

(i)     correct substitution     (A1)

eg\(\;\;\;6 \times 2 + 3 \times 2 + 6 \times 1\)

\(u \bullet v = 24\)     A1     N2

(ii)     correct substitution into magnitude formula for \({{u}}\) or \({{v}}\)     (A1)

eg\(\;\;\;\sqrt {{6^2} + {3^2} + {6^2}} ,{\text{ }}\sqrt {{2^2} + {2^2} + {1^2}} \), correct value for \(\left| {{v}} \right|\)

\(\left| {{u}} \right| = 9\)     A1     N2

(iii)     \(\left| {{v}} \right| = 3\)     A1     N1

[5 marks]

a.

correct substitution into angle formula     (A1)

eg\(\;\;\;\frac{{24}}{{9 \times 3}},{\text{ }}0.\bar 8\)

\(0.475882,{\text{ }}27.26604^\circ \)     A1     N2

\(0.476,{\text{ }}27.3^\circ \)

[2 marks]

Total [7 marks]

b.

Examiners report

Many candidates performed well in this question. Some candidates were unfamiliar with the basis vector notation and wrongly substituted the i-j-k into the formulas. Others occasionally assumed that the magnitude could be negative.

a.

Many candidates performed well in this question. Some candidates were unfamiliar with the basis vector notation and wrongly substituted the i-j-k into the formulas. Others occasionally assumed that the magnitude could be negative.

b.

Syllabus sections

Topic 4 - Vectors » 4.2 » The scalar product of two vectors.
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