Find the equation of a line passing through the point `(2,-3,5)` and parallel to vector `(3hati+2hatj-hatk)`.

Explanation

To find the equation of a line passing through the point \( (2, -3, 5) \) and parallel to the vector \( \vec{b} = 3\hat{i} + 2\hat{j} - \hat{k} \), we can follow these steps:

### Step 1: Identify the point and direction vector
The point through which the line passes is given as \( (x_1, y_1, z_1) = (2, -3, 5) \). The direction vector \( \vec{b} \) has components \( (b_1, b_2, b_3) = (3, 2, -1) \).

### Step 2: Write the general equation of the line
The equation of a line in three-dimensional space can be expressed in the symmetric form:
\[
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