Let's break down the given information and solve each part of the problem:

Given:

• We are given the vector and the point C (1, 3, 4), but the vector information for points A and B is missing in your message. I will assume that vectors A and B are two points in 3D space. To proceed, please confirm or provide the coordinates for points A and B.

Once we have the coordinates of A and B, we can do the following:

(i) Vector AB (R vector AB)

To find the vector AB, we will subtract the coordinates of point A from the coordinates of point B: $\mathbf{R_{AB}} = \mathbf{B} - \mathbf{A}$

(ii) Vector AC (R vector AC)

To find the vector AC, we subtract the coordinates of point A from the coordinates of point C: $\mathbf{R_{AC}} = \mathbf{C} - \mathbf{A}$

(iii) Unit vector directed from C to A

The unit vector is a vector with a magnitude of 1, which points in the direction from point C to point A. To calculate it:

1. First find the vector CA by subtracting the coordinates of point C from point A.
2. Then divide the vector by its magnitude to get the unit vector.

The magnitude of a vector $\mathbf{R}$ is given by: $|\mathbf{R}| = \sqrt{R_x^2 + R_y^2 + R_z^2}$ where $R_x, R_y, R_z$ are the components of the vector.

The unit vector $\hat{\mathbf{R}}$ is: $\hat{\mathbf{R}} = \frac{\mathbf{R}}{|\mathbf{R}|}$

Let me know the coordinates for points A and B so I can proceed with the calculations.