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

|

4 i + 2 j

| =

4.47214

and

|

–2 i + 2 j

| = 2.82843

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

cos(α) =

–4 4.47214×2.82843

= –0.316

to 3 dps.

Since the angle and its cosine can be measured clockwise or anticlockwise, the answer 0.316 is also correct.