Explanation:

Let’s break this down:

- The given plane equation is:

\( \frac{2x}{k} + \frac{2y}{3} + \frac{z}{3} = 2 \)

- To find the direction ratios (DRs) of the normal, rewrite in standard form:

\( \frac{2}{k}x + \frac{2}{3}y + \frac{1}{3}z - 2 = 0 \)

The DRs of the normal are coefficients of x, y, z:

\( \left\langle \frac{2}{k}, \frac{2}{3}, \frac{1}{3} \right\rangle \)

- But they haven’t given k. For DRs, any proportional set will work.

- Check options for matching the pattern \(\langle 2/k, 2/3, 1/3 \rangle\):

- Option 1: <3, 2, 1>

- Option 2: <2, 3, 6>

- Option 3: <6, 3, 2>

- Option 4: <1, 2, 3>

- Multiply option 1 by 1/3 and get <1, 2/3, 1/3>, which matches the coefficients if k=2/3, up to proportionality.

- Options 2, 3, and 4 don’t match the ratios directly or proportionally.

Option 1: <3, 2, 1> is correct

- Remember, the direction ratios of the normal are just the coefficients of x, y, z (or any proportional set).

- The rest don’t fit the structure.

That’s really all there is to it.