If $\vec{a}$ and $\vec{b}$ are reciprocal vectors, then : |
$\vec{a} . \vec{b} = 0$ $\vec{a} . \vec{b} = -1$ $\vec{a} . \vec{b} = 1$ None of these |
$\vec{a} . \vec{b} = 1$ |
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. |