18M.1.AHL.TZ2.H_1

pestleMathematicsAAHLPaper 118M· ahl-3-13-scalar-(dot)-productsource ↗

The acute angle between the vectors 3i − 4j − 5k and 5i − 4j + 3k is denoted by θ.

Find cos θ.

Markscheme / solution

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

cos θ = $\frac{{\left( {3i - 4j - 5k} \right) \bullet \left( {5i - 4j + 3k} \right)}}{{\left| {3i - 4j - 5k} \right|\left| {5i - 4j + 3k} \right|}}$ (M1)

$= \frac{{16}}{{\sqrt {50} \sqrt {50} }}$ A1A1

Note: A1 for correct numerator and A1 for correct denominator.

$= \frac{8}{{25}}\left( { = \frac{{16}}{{50}} = 0.32} \right)$ A1

[4 marks]

Examiners’ report

[N/A]