 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-2/1/solution

a \cdot b = - 1 + 2 + 3 = 4

, while the Euclidean norms are

3

and

14

. Thus the angle in the stated range is

θ = arccos \frac{4}{42} .

The positive cosine shows that it is an acute angle.

 New to topics? Read the docs here!