When `A.B =-|A||B|,` then

Options

A. A and B are perpendicular to each other
B. A and B act in the same direction
C. A and B act in the opposite sirection
D. A and B can act in any in any direction

Explanation

To solve the problem, we need to analyze the given equation \( A \cdot B = -|A||B| \).

### Step-by-step Solution:

1. **Understanding the Dot Product**:
The dot product of two vectors \( A \) and \( B \) can be expressed as:
\[ A \cdot B = |A||B|\cos\theta \]
where \( \theta \) is the angle between the two vectors.

2. **Setting Up the Equation**:
According to the problem, we have:
\[ A \cdot B = -|A||B| \]
By substituting the expression for the dot product, we get:
\[ |A||B|\cos\theta = -|A||B| \]

3. **Dividing Both Sides**:
Assuming \( |A| \) and \( |B| \) are both non-zero (since they are magnitudes of vectors), we can divide both sides by \( |A||B| \):
\[ \cos\theta = -1 \]

4. **Finding the Angle**:
The equation \( \cos\theta = -1 \) indicates that:
\[ \theta = 180^\circ \]
This means that the vectors \( A \) and \( B \) are pointing in exactly opposite directions.

5. **Conclusion**:
Since \( A \) and \( B \) are acting in opposite directions, the correct answer is that they act in opposite directions.

### Final Answer:
The correct option is **Option 3: A and B act in opposite directions**.

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