Express the vector joining the two points $A(0, 1, 2)$ and $B(1, 4, 4)$ as the sum of the components along $x$, $y$ and $z$ axes using unit vectors $\hat{i}, \hat{j}$ and $\hat{k}$, i.e., vector $\vec{AB} = x\hat{i} + y\hat{j} + z\hat{k}$.

$\hat{i} + 3\hat{j} + 2\hat{k}$

The correct answer is Option (2) → $\hat{i} + 3\hat{j} + 2\hat{k}$ ##

The position vectors of $A$ and $B$ are:

$\vec{OA} = 0\hat{i} + \hat{j} + 2\hat{k}$

and $\vec{OB} = \hat{i} + 4\hat{j} + 4\hat{k}$

$\vec{AB} = \vec{OB} - \vec{OA}$

$\vec{AB} = (\hat{i} + 4\hat{j} + 4\hat{k}) - (0\hat{i} + \hat{j} + 2\hat{k})$

$\vec{AB} = \hat{i} + 3\hat{j} + 2\hat{k}$