This problem involves a rectangular prism and requires us to calculate diagonal distances using the Pythagorean theorem.

Let's break this into steps:

(a) Find $a$:

To find $a$, the diagonal across the base of the rectangular prism, we use the Pythagorean theorem in two dimensions: $a = \sqrt{l^2 + w^2}$ where $l$ is the length and $w$ is the width of the base.

(b) Find $b$:

Once $a$ (the diagonal of the base) is known, we can use it to find $b$, the diagonal of the entire rectangular prism. Here, $b$ is the space diagonal, calculated using the 3D version of the Pythagorean theorem: $b = \sqrt{a^2 + h^2}$ where $h$ is the height of the prism.

Can you confirm the dimensions of the rectangular prism (length, width, height)? This will help me proceed with the calculations.