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Q. $ \overrightarrow{a}[\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{b})] $ is equal to

Rajasthan PETRajasthan PET 2001

Solution:

$ \overrightarrow{a}\times [\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{b})]=\overrightarrow{a}\times [(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{a}-(\overrightarrow{a}.\overrightarrow{a})\overrightarrow{b}] $
$ =-(\overrightarrow{a}.\overrightarrow{a})(\overrightarrow{a}\times \overrightarrow{b}) $
$ =(\overrightarrow{a}.\overrightarrow{a})(\overrightarrow{b}\times \overrightarrow{a}) $