Study the following graph carefully and answer the questions that follow :

| Aspect | Stage I (High Fluctuating) | Stage III (Low Fluctuating) |
|---|---|---|
| Characteristics | High birth rates and high death rates, resulting in low population growth. | Low birth rates and low death rates, resulting in very low population growth or decline. |
| Causes | Poor healthcare, high infant mortality, limited food/resources, frequent epidemics. | Advanced healthcare, contraception use, higher education, economic development. |
| Examples | Rainforest tribes, remote communities. | Developed countries like Canada, Japan, USA. |
| Birth Rate | High | Low |
| Death Rate | High | Low |
| Population Growth | Low | Very low or stable |
| Socio-economic Conditions | Primitive or underdeveloped | Highly developed |
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?