Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to the plane `3x-4y+5z=8.`

Explanation

To find the vector equation of a line that passes through a specific point and is perpendicular to a given plane, we can follow these steps:

### Step 1: Identify the point and the plane
The line passes through the point given by the position vector:
\[ \mathbf{A} = 3\hat{i} - 5\hat{j} + 7\hat{k} \]
The equation of the plane is:
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