Let $\vec a$ be a non-zero vector of magnitude 'a' and $λ$ is a non-zero scalar, then $λ\vec a$ is a unit vector if
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $a=\frac{1}{|λ|}$
Given:
$|\vec{a}| = a$, and $\lambda$ is a scalar.
For $\lambda \vec{a}$ to be a unit vector, its magnitude must be 1:
$|\lambda \vec{a}| = 1$
$|\lambda| \, |\vec{a}| = 1$
$|\lambda| \, a = 1$
$|\lambda| = \frac{1}{a}$
Therefore, $\lambda a⃗$ is a unit vector if $|\lambda| = \frac{1}{a}$.