Find the vector and the Cartesian equations of the line through the point `(5, 2, 4)`and which is parallel to the vector `3 hat i+2 hat j-8 hat k`.

Explanation

To find the vector and Cartesian equations of the line that passes through the point \( (5, 2, 4) \) and is parallel to the vector \( 3\hat{i} + 2\hat{j} - 8\hat{k} \), we can follow these steps:

### Step 1: Identify the point and direction vector
The line passes through the point \( A(5, 2, 4) \) and is parallel to the vector \( \mathbf{B} = 3\hat{i} + 2\hat{j} - 8\hat{k} \).

### Step 2: Write the vector equation of the line
The vector equation of a line in space can be expressed as:
\[
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