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Question
If \[\left| \vec{a} \right| = \left| \vec{b} \right|, \text{ then } \left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) =\]
Options
(a) positive
(b) negative
(c) 0
(d) None of these
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Solution
(c) 0
\[\text{ Given that }\]
\[\left| \vec{a} \right| = \left| \vec{a} \right|\]
\[ \Rightarrow \left( \vec{a} + \vec{b} \right) . \left( \vec{a} - \vec{b} \right) = \left| \vec{a} \right|^2 - \left| \vec{b} \right|^2 \]
\[ = \left| \vec{a} \right|^2 - \left| \vec{a} \right|^2 \]
\[ = 0\]
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