 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/11/a/solution

a \times b = \hat{k}

, so

(a \times b) \times c = \hat{k} \times \hat{k} = 0.

On the other hand,

b \times c = \hat{i} - \hat{j}

and hence

a \times (b \times c) = \hat{i} \times (\hat{i} - \hat{j}) = - \hat{k} .

These results are unequal, proving that the cross product does not satisfy the associative property.

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