Assertion : The direction of a zero (null) vector is indeteminate.
Reason : We can have `vecAxx vecB = vecA *vecB` with `vecA ne vec0 and vecB ne vec0`.

Options

A. `[M^(0)L^(2)T^(0)]`
B. `[ML^(2)T]`
C. `[ML^(0)T^(-1)]`
D. `[M^(0)L^(2)T^(-1)]`

Explanation

To solve the question, we need to analyze the assertion and the reason given.

### Step 1: Understand the Assertion
The assertion states that "The direction of a zero (null) vector is indeterminate."
- A zero vector is defined as a vector with zero magnitude.
- Since it has no length, it does not point in any specific direction. Therefore, we can conclude that the assertion is true.

### Step 2: Understand the Reason
The reason provided is: "We can have \(\vec{A} \times \vec{B} = \vec{A} \cdot \vec{B}\) with \(\vec{A} \neq \vec{0}\) and \(\vec{B} \neq \vec{0}\)."
- The cross product \(\vec{A} \times \vec{B}\) results in a vector that is perpendicular to both \(\vec{A}\) and \(\vec{B}\). Its magnitude is given by \(|\vec{A}||\vec{B}|\sin(\theta)\), where \(\theta\) is the angle between the two vectors.
- The dot product \(\vec{A} \cdot \vec{B}\) results in a scalar value, calculated as \(|\vec{A}||\vec{B}|\cos(\theta)\).
- Since one is a vector and the other is a scalar, they cannot be equal. Therefore, the reason is false.

### Step 3: Conclusion
Based on the analysis:
- The assertion is true: The direction of a zero vector is indeed indeterminate.
- The reason is false: The equation \(\vec{A} \times \vec{B} = \vec{A} \cdot \vec{B}\) cannot hold true for non-zero vectors.

### Final Answer:
- Assertion: True
- Reason: False

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