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

Find cos θ.

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]