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 

Answer 1

(c) 0  
\[\text{ Given that }\]
\[\left| \vec{a} \right| = \left| \vec{a} \right|\]
\[ \Rightarrow \left( \vec{a} + \vec{b} \right) . \left( \vec{a} - \vec{b} \right) = \left| \vec{a} \right|^2 - \left| \vec{b} \right|^2 \]
\[ = \left| \vec{a} \right|^2 - \left| \vec{a} \right|^2 \]
\[ = 0\]