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Q4  Show that ( \vec a - \vec b ) \times (\vec a + \vec b ) = 2 ( \vec a \times \vec b )

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best_answer

To show that ( \vec a - \vec b ) \times (\vec a + \vec b ) = 2 ( \vec a \times \vec b )

LHS=

\\( \vec a - \vec b ) \times (\vec a + \vec b )=( \vec a - \vec b ) \times (\vec a)+( \vec a - \vec b ) \times (\vec b)

( \vec a - \vec b ) \times (\vec a + \vec b )= \vec a \times \vec a-\vec b \times\vec a+\vec a \times \vec b-\vec b \times \vec b

As product of a vector with itself is always Zero,

( \vec a - \vec b ) \times (\vec a + \vec b )= 0-\vec b \times\vec a+\vec a \times \vec b-\0

As cross product of a and b is equal to negative of cross product of b and a.

( \vec a - \vec b ) \times (\vec a + \vec b )= \vec a \times\vec b+\vec a \times \vec b

( \vec a - \vec b ) \times (\vec a + \vec b )= 2(\vec a \times\vec b)= RHS

 LHS is equal to RHS, Hence Proved.

 

Posted by

Pankaj Sanodiya

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