Consider the following
1. `4hat(i) xx 3hat(i) = 0` II. `(4hat(i))/(3hat(i))= (4)/(3)`
Which of the above statements is/are correct?

Options

A. Only I
B. Only II
C. Both I and II
D. Neither I nor II

Answer

To determine which of the statements is correct, we will analyze each statement step by step.

**Step 1: Analyze Statement I**
- The first statement is: \( 4\hat{i} \times 3\hat{i} = 0 \).
- Here, we are performing the cross product of two vectors \( 4\hat{i} \) and \( 3\hat{i} \).
- Recall that the cross product of any vector with itself is zero. Therefore, \( \hat{i} \times \hat{i} = 0 \).
- Thus, \( 4\hat{i} \times 3\hat{i} = 12(\hat{i} \times \hat{i}) = 12 \cdot 0 = 0 \).
- Therefore, Statement I is **correct**.

**Step 2: Analyze Statement II**
- The second statement is: \( \frac{4\hat{i}}{3\hat{i}} = \frac{4}{3} \).
- Here, we are trying to simplify the expression \( \frac{4\hat{i}}{3\hat{i}} \).
- However, when dividing vectors, we cannot simply cancel out the unit vectors like scalars. The operation is not valid in vector algebra.
- Therefore, \( \frac{4\hat{i}}{3\hat{i}} \) does not equal \( \frac{4}{3} \) because this operation is meaningless.
- Thus, Statement II is **incorrect**.

**Final Conclusion**
- From our analysis, we find that:
- Statement I is correct.
- Statement II is incorrect.
- Therefore, the correct answer is that **only Statement I is correct**.