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 + r k).(t i + u j + v k) = p×t + q×u + r×v

cos(α) =

a.b |a| |b|

The two vectors in this question have lengths

5.38516

and

2.82843

The dot product of the two vectors is (–2)×2 + 4×(–2) + 3×0 = –12

cos(α) =

–12 5.38516×2.82843

= –0.788

to 3 dps.

Since the angle and its cosine can be measured clockwise or anticlockwise, the answer 0.788 is also correct.