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Expansion of (a-b)^3

Write the val...

Question

Write the value of $\hat{i} . (\hat{j} \times \hat{k}) + \hat{j} . (\hat{k} \times \hat{i}) + \hat{k} . (\hat{i} \times \hat{j}) .$

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Solution

$\hat{i} . (\hat{j} \times \hat{k}) + \hat{j} . (\hat{k} \times \hat{i}) + \hat{k} . (\hat{i} \times \hat{j}) = \hat{i} . \hat{i} + \hat{j} . j + \hat{k} . \hat{k} = {|\hat{i}|}^{2} + {|\hat{j}|}^{2} + {|\hat{k}|}^{2} = 1 + 1 + 1 = 3$

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