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Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 1 / 5B / a / i / Solution

For

A = (A_{1}, A_{2}, A_{3})

and

B = (B_{1}, B_{2}, B_{3})

, the scalar product is the inner product

A \cdot B = A_{1} B_{1} + A_{2} B_{2} + A_{3} B_{3} .

The cross product is

A \times B = (A_{2} B_{3} - A_{3} B_{2},, A_{3} B_{1} - A_{1} B_{3},, A_{1} B_{2} - A_{2} B_{1}) .

It is perpendicular to both vectors and has magnitude

∣ A ∣∣ B ∣ sin θ

.

Solved by gpt-5.6-sol high.

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