Consider the following :
1. `4hat(i)xx3hat(i)=hat(0) " " 2. (4hat(i))/(3hat(i))=(4)/(3)`
Which of the above is/are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To determine the correctness of the two statements given, we will analyze each one step by step.

### Step 1: Analyze the first statement
The first statement is:
\[ 4\hat{i} \times 3\hat{i} = \hat{0} \]

#### Explanation:
- The expression \( \hat{i} \) represents a unit vector in the x-direction.
- The cross product of two vectors is given by:
\[ \mathbf{A} \times \mathbf{B} = |\mathbf{A}||\mathbf{B}|\sin(\theta) \hat{n} \]
where \( \theta \) is the angle between the two vectors and \( \hat{n} \) is the unit vector perpendicular to the plane containing \( \mathbf{A} \) and \( \mathbf{B} \).
- In this case, both vectors are \( 4\hat{i} \) and \( 3\hat{i} \), which are parallel (same direction). Therefore, the angle \( \theta = 0^\circ \).
- Since \( \sin(0^\circ) = 0 \), we have:
\[ 4\hat{i} \times 3\hat{i} = 0 \]

#### Conclusion for Step 1:
Thus, the first statement is correct:
\[ 4\hat{i} \times 3\hat{i} = \hat{0} \]

### Step 2: Analyze the second statement
The second statement is:
\[ \frac{4\hat{i}}{3\hat{i}} = \frac{4}{3} \]

#### Explanation:
- The division of vectors is not defined in the same way as scalar division. However, we can analyze the expression.
- When dividing two vectors that are in the same direction, we can consider their magnitudes:
\[ \frac{4\hat{i}}{3\hat{i}} = \frac{4}{3} \hat{i} \]
- This means that the division results in a scalar multiplied by the direction of the unit vector \( \hat{i} \).

#### Conclusion for Step 2:
Thus, the second statement is incorrect because it does not yield a scalar but rather a vector:
\[ \frac{4\hat{i}}{3\hat{i}} \neq \frac{4}{3} \]

### Final Conclusion:
- The first statement is correct.
- The second statement is incorrect.

### Summary:
- **First Statement:** Correct
- **Second Statement:** Incorrect