Vectors: Angle between two vectors

Worked Solution:

The dot product (scalar product) of two vectors a and b is :

a.b = |a| |b| cos(α) where α is the angle between the vectors, and also
(p i + q j).(t i + u j) = p×t + q×u

cos(α) =

a.b |a| |b|

The two vectors in this question have lengths

8.06226

and

7.81025

The dot product of the two vectors is (–1)×(–5) + 8×(–6) = –43

cos(α) =

–43 8.06226×7.81025

= –0.683

to 3 dps.

Since the angle and its cosine can be measured clockwise or anticlockwise, the answer 0.683 is also correct.