 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/7/solution

The two directed segments have vectors

u = (1, 0, - 1)

and

v = (0, 1, 1)

. Their dot product is

- 1

and both norms equal

2

. Hence

cos θ = \frac{u \cdot v}{∣ u ∣∣ v ∣} = - \frac{1}{2}, θ = \frac{2 π}{3} = 12 0^{\circ} .

The common starting point fixes the obtuse angle between these segments.

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