Find the vector equation of the line through `A(3,4,-7)a n dB(1,-1,6)dot` Find also, its Cartesian equations.

Explanation

To find the vector equation of the line through points A(3, 4, -7) and B(1, -1, 6), we can follow these steps:

### Step 1: Identify the position vectors of points A and B
The position vector of point A is:
\[ \vec{A} = 3\hat{i} + 4\hat{j} - 7\hat{k} \]
The position vector of point B is:
...