Find the equations of the two lines through the origin which intersect the line `(x-3)/2=(y-3)/1=z/1` at angle of `pi/3` each.

Explanation

To find the equations of the two lines through the origin that intersect the line \(\frac{x-3}{2} = \frac{y-3}{1} = z\) at an angle of \(\frac{\pi}{3}\), we can follow these steps:

### Step 1: Determine the direction ratios of the given line
The given line can be expressed in parametric form. From the equation \(\frac{x-3}{2} = \frac{y-3}{1} = z\), we can let \(k\) be the parameter:
- \(x = 2k + 3\)
- \(y = k + 3\)
- \(z = k\)

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