Explanation:

Let’s break down what’s going on with this plane:

- The plane’s equation: (2x)/k + (2y)/3 + (z)/3 = 2.

- It passes through (2, 3, -6).

- The intercepts on the x, y, z axes are p, q, r.

- You’re asked what (p + q + r) equals.

Let’s unpack the steps:

- First, plug in (2, 3, -6) into the equation:

(2×2)/k + (2×3)/3 + (-6)/3 = 2

(4)/k + 2 + (-2) = 2

(4)/k = 2 ? k = 2

- So, new plane: x + (2y)/3 + (z)/3 = 2

- Now, find intercepts:

- x-intercept: set y = 0, z = 0 ? x = 2 ? p = 2

- y-intercept: x = 0, z = 0 ? (2y)/3 = 2 ? 2y = 6 ? y = 3 ? q = 3

- z-intercept: x = 0, y = 0 ? z/3 = 2 ? z = 6 ? r = 6

- Add them: p + q + r = 2 + 3 + 6 = 11

Now, let’s look at the options:

- Option 1: 10

- Option 2: 11

- Option 3: 12

- Option 4: 13

Option 2 (11) is correct.