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Q6   Find |\vec a| \: \: and\: \:| \vec b | , if ( \vec a + \vec b ). ( \vec a - \vec b )=8 \: \:and \: \: |\vec a |\: \:= 8 \: \:|\vec b |.

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Given in the question

( \vec a + \vec b ). ( \vec a - \vec b )=8

\left | \vec a \right |^2-\left | \vec b \right |^2=8

Since |\vec a |\: \:= 8 \: \:|\vec b |

\left | \vec {8b} \right |^2-\left | \vec b \right |^2=8

\left | \vec {63b} \right |^2=8

\left | \vec {b} \right |^2=\frac{8}{63}

\left | \vec {b} \right |=\sqrt{\frac{8}{63}}

So, answer of the question is

\left | \vec {a} \right |=8\left | \vec {b} \right |=8\sqrt{\frac{8}{63}}

Posted by

Pankaj Sanodiya

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