Find `alpha and beta ` if the force `vec(F) = 2hat(i) - 3hat(j) +hat(k)` acting at `(2,beta,-1)` produces no torque about `(alpha,0,2)`

Explanation

To find the values of \( \alpha \) and \( \beta \) such that the force \( \vec{F} = 2\hat{i} - 3\hat{j} + \hat{k} \) acting at the point \( (2, \beta, -1) \) produces no torque about the point \( (\alpha, 0, 2) \), we can follow these steps:

### Step 1: Define the Position Vectors
Let:
- \( \vec{r_1} = (\alpha, 0, 2) \) (the point about which we are calculating torque)
- \( \vec{r_2} = (2, \beta, -1) \) (the point where the force is applied)

The position vector \( \vec{r} \) from \( \vec{r_1} \) to \( \vec{r_2} \) is given by:
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