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Cinque Terre

Given , \(\mid\overrightarrow a\mid=1,\mid\overrightarrow b\mid=1,\mid\overrightarrow c\mid=2\)

⇒   \(\overrightarrow a\times(\overrightarrow a\times\overrightarrow c)+\overrightarrow b=0\)

⇒   \((\overrightarrow a.\overrightarrow c)\overrightarrow a-(\overrightarrow a.\overrightarrow a)\overrightarrow c+\overrightarrow b=0\)

⇒   \((\mid\overrightarrow a\mid \mid\overrightarrow c\mid cos\theta )\overrightarrow a-\mid\overrightarrow a\mid^2\overrightarrow c+\overrightarrow b=0\)

⇒   \(2 cos\theta \overrightarrow a-\overrightarrow c+\overrightarrow b=0\)

⇒   \(\mid\overrightarrow b\mid=\mid\overrightarrow c-2 cos\theta \overrightarrow a\mid\)

⇒   \(1=4+4cos^2\theta-4cos\theta(2cos\theta)\)

so , \(cos\theta={\sqrt3\over2}\)

then, \(\theta ={\pi\over6}\)

correct answer is (c).



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