Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes `vecr*(hati-hatj+2hatk)=5 and vecr*(3hati+hatj+hatk)=6`.

Explanation

To find the vector equation of the line passing through the point (1, 2, 3) and parallel to the given planes, we can follow these steps:

### Step 1: Identify the normal vectors of the planes
The equations of the planes are given as:
1. \(\vec{r} \cdot (\hat{i} - \hat{j} + 2\hat{k}) = 5\)
2. \(\vec{r} \cdot (3\hat{i} + \hat{j} + \hat{k}) = 6\)

From these equations, we can extract the normal vectors of the planes:
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