If $\vec{a}$ and $\vec{b}$ are reciprocal vectors, then :
Answer & explanation
Correct answer: option 3
If $\vec{a}$ and $\vec{b}$ are reciprocal, then
$\vec{a}=\lambda \vec{b}, \lambda \in R^{+}$ and $|\vec{a}||\vec{b}|=1$
$\Rightarrow|\vec{a}|=|\lambda||\vec{b}|$
$\Rightarrow|\lambda|=\frac{|\vec{a}|}{|\vec{b}|}=\frac{1}{|\vec{b}|^2}$
$\Rightarrow|\vec{a}|=\frac{1}{|\vec{b}|^2} \vec{b}$
$\Rightarrow \vec{a} \cdot \vec{b}=\frac{1}{|\vec{b}|^2}|\vec{b}||\vec{b}| \cos 0=1$
Hence (3) is correct answer.