Question

If $\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|,\mathrm{then}\left(\overrightarrow{a}+\overrightarrow{b}\right)·\left(\overrightarrow{a}-\overrightarrow{b}\right)=$
(a) positive
(b) negative
(c) 0
(d) None of these

Answer 1

(c) 0

$$\begin{gathered} \text{Given that} \\ \left|\overrightarrow{a}\right|=\left|\overrightarrow{a}\right| \\ \Rightarrow \left(\overrightarrow{a}+\overrightarrow{b}\right).\left(\overrightarrow{a}-\overrightarrow{b}\right)={\left|\overrightarrow{a}\right|}^2-{\left|\overrightarrow{b}\right|}^2 \\ ={\left|\overrightarrow{a}\right|}^2-{\left|\overrightarrow{a}\right|}^2 \\ =0 \end{gathered}$$