 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/3/b/solution

Since

v = - u

and

u \neq = 0

, the vectors point in opposite directions. More explicitly, their dot product gives

cos θ = \frac{u \cdot v}{∥ u ∥∥ v ∥} = - 1.

Hence their angle is

θ = π radians = 18 0^{\circ}

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