Question
Show that $\vec{A}=\frac{\hat{i}-\hat{j}}{\sqrt{2}}$ is a unit vector.

Answer

Let $\hat{a}$ be unit vector of $s \vec{a}$.
$\therefore \quad \hat{a}=\frac{\vec{a}}{|\vec{a}|}$
Now, $|\vec{a}|=\sqrt{a_x^2+a_y^2}=\sqrt{\left(\frac{1}{\sqrt{2}}\right)^2+\left(\frac{-1}{\sqrt{2}}\right)^2}=1$
$\therefore \quad \hat{a}=\frac{\vec{a}}{1} \Rightarrow \vec{a}$ itself is a unit vector.

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