# If $$\overrightarrow a$$ is a nonzero vector of magnitude $" a "$ and $$λ$$ a nonzero scalar, then $$λ$$ $$\overrightarrow a$$ is unit vector if

$\begin{array} (A)\; λ = 1 \quad & (B)\; λ = -1 \quad & (C)\; a = |\; λ\; | \quad & (D)\; a = 1/|\; λ\; | \end{array}$

Toolbox:
• A vector is said to be unit vector if its magnitude is 1.
Step 1:
Given :$\overrightarrow a$ is a non-zero vector of magnitude "a"
(i.e) $\mid\overrightarrow a=a$.
$|\lambda\overrightarrow a|=1$ is a unit vector if $|\lambda\overrightarrow a|=1$ or $|\lambda||\overrightarrow a|=1$
Step 2:
But $|\overrightarrow a|=a$
Hence $|\lambda|a=1$
$\Rightarrow a=\large\frac{1}{|\lambda|}$
Hence (D) is the correct option.