Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Vectors

Question:

If $\vec{a}$ and $\vec{b}$ are reciprocal vectors, then :

Options:

$\vec{a} . \vec{b} = 0$

$\vec{a} . \vec{b} = -1$

$\vec{a} . \vec{b} = 1$

None of these

Correct Answer:

$\vec{a} . \vec{b} = 1$

Explanation:

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.