The angle \( \theta \) between two non-zero vectors \( a \) and \( b \) satisfies the relation \...

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The angle \( \theta \) between two non-zero vectors \( a \) and \( b \) satisfies the relation
\[
\cos \theta=(a \times \hat{i}) \cdot(b \times \hat{i})+(a \times \hat{j}) \cdot(b \times \hat{j})+(a \times \hat{k}) \cdot(b \times \hat{k})
\]
then the least value of \( |a|+|b| \) is equal to (where \( \theta \neq 90^{\circ} \) )
(a) \( \frac{1}{2} \)
(b) 2
(c) \( \sqrt{2} \)
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