Let , and . Then the value of , such that ( a b ) ( b c ) ( c a ) = 0,…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

\mathbf{a} = \alpha\hat{i} + 2\hat{j} - 3\hat{k}

,

\mathbf{b} = \hat{i} + 2\alpha\hat{j} - 2\hat{k}

and

\mathbf{c} = 2\hat{i} - \alpha\hat{j} + \hat{k}

. Then the value of

6\alpha

, such that

\left\{(\mathbf{a} \times \mathbf{b}) \times (\mathbf{b} \times \mathbf{c})\right\} \times (\mathbf{c} \times \mathbf{a}) = 0, \text{ is}

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