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$Let \bar{a}, \bar{b}, \bar{c} be three vectors such that | \vec{a} | = 1, | \bar{b} | = 1 and | \bar{c} | = 2 and if \bar{a} \times (\bar{a} \times \bar{c}) + \bar{b} = \bar{0}, then$
$angle between \bar{a} and \bar{c} can be$

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π6

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detailed solution

Correct option is C

a¯×(a¯×c¯)+b¯=0¯(a¯⋅c¯)a¯−(a¯⋅a¯)c¯+b¯=0¯(a¯⋅c¯)a¯−c¯=−b¯Ka¯−c¯=−b¯, where K=a.bK2a¯2+c¯2−2K2=b¯2K=±3⇒cos⁡θ=±32

Similar Questions

$A particle acted on by constant forces \bar{f} = 4 \hat{i} + 3 \hat{j} - 3 \hat{k}$ $and \vec{g} = 3 \hat{i} + \hat{j} - \hat{k} experiences a displacement from the$ $point \vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k} to the point \vec{b} = 5 \hat{i} + 4 \hat{j} + \hat{k} . The total$ $work done by the forces is$

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