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

10.81665

and

7.07107

The dot product of the two vectors is (–6)×1 + (–9)×(–7) = 57

cos(α) =

57 10.81665×7.07107

= 0.745

to 3 dps.

Since the angle and its cosine can be measured clockwise or anticlockwise, the answer –0.745 is also correct.