**Solution:**

To find the value of $a$ in the given equation $2x^2 - 3xy - ay^2 = 0$, we need to consider the condition for the equation to represent two perpendicular lines.

The given equation represents two lines when the discriminant of the equation is zero.

**1. Finding the Discriminant:**

The discriminant ($D$) of a quadratic equation $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ is given by the formula:

$D = B^2 - 4AC$

Comparing the given equation $2x^2 - 3xy - ay^2 = 0$ with the general form, we have:

$A = 2, B = -3, C = -a$

Substituting the values into the discriminant formula:

$D = (-3)^2 - 4(2)(-a)$

Simplifying,

$D = 9 + 8a$

**2. Condition for Perpendicular Lines:**

For the given equation to represent two perpendicular lines, the discriminant $D$ must be equal to zero.

$D = 0$

$9 + 8a = 0$

Solving the equation,

$8a = -9$

$a = -\frac{9}{8}$

Therefore, the value of $a$ is $-\frac{9}{8}$.

**3. Finding the Value of $b$ and $2$:**

The equation $2x^2 - 3xy - ay^2 = 0$ represents two perpendicular lines with the value of $a$ as $-\frac{9}{8}$. However, the equation also contains the term $x\cdot by$, which suggests that the coefficient of $xy$ is $b$.

Comparing the given equation with the general form, we have:

$B = -3$

Therefore, the value of $b$ is $-3$.

Similarly, there is no term involving $x^2$, so the coefficient of $x^2$ is $0$. Hence, the value of $2$ is $0$.

Therefore, the value of $a$ is $-\frac{9}{8}$, the value of $b$ is $-3$, and the value of $2$ is $0$.