Step 1: Functions of the lac operon genes.
- 'i' gene: Produces the repressor protein (iii).
- 'z' gene: Produces $\beta$-galactosidase (i), which breaks down lactose.
- 'a' gene: Produces transacetylase (iv).
- 'y' gene: Produces lac permease (ii), which facilitates lactose entry into the cell.
| List I | List II | ||
|---|---|---|---|
| A | Two or more alternative forms of a gene | I | Back cross |
| B | Cross of F1 progeny with homozygous recessive parent | II | Ploidy |
| C | Cross of F progeny with any of the parents | III | Allele |
| D | Number of chromosome sets in plant | IV | Test cross |

If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?