 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/3/b/solution

The cross product has magnitude

∣ a ∣∣ b ∣ sin θ

, where

θ

is their angle. Therefore

It is the area of the parallelogram spanned by the two vectors.

The area is zero if the vectors are parallel or either is zero. The corresponding triangle has half this area.

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