Given the position vectors OA = 7i + 3j − k and OB = 2i − 5j + 4k, find the magnitude of vector AB.

The position vector of point A is $\vec{OA} = 7\hat{i} + 3\hat{j} - \hat{k}$.
The position vector of point B is $\vec{OB} = 2\hat{i} - 5\hat{j} + 4\hat{k}$.

The vector $\vec{AB}$ is found by subtracting the position vector of A from the position vector of B:

The magnitude of a vector $x\hat{i} + y\hat{j} + z\hat{k}$ is given by $\sqrt{x^2 + y^2 + z^2}$.

The calculated magnitude is $\sqrt{114}$. This matches option (b).

The final answer is $\text{(b)} \sqrt{114}$.