If `overset(rarr)B=noverset(rarr)A` and `overset(rarr)A` is antiparallel with `overset(rarr)B`, then n is :

Options

A. a vector
B. negative and dimensions less
C. a scalar
D. a negative scalar

Explanation

To solve the problem, we need to analyze the relationship between the vectors \(\overset{\rarr}{B}\) and \(\overset{\rarr}{A}\) given the conditions stated in the question.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We are given that \(\overset{\rarr}{B} = n \overset{\rarr}{A}\) and that \(\overset{\rarr}{A}\) is antiparallel to \(\overset{\rarr}{B}\).

2. **Definition of Antiparallel Vectors**:
Antiparallel vectors are vectors that point in opposite directions. For two vectors \(\overset{\rarr}{A}\) and \(\overset{\rarr}{B}\) to be antiparallel, the scalar \(n\) must be negative.

3. **Setting Up the Equation**:
From the relationship \(\overset{\rarr}{B} = n \overset{\rarr}{A}\), we can infer that if \(\overset{\rarr}{A}\) has a certain magnitude and direction, then \(\overset{\rarr}{B}\) will have the same magnitude but opposite direction when \(n\) is negative.

4. **Conclusion About \(n\)**:
Since \(\overset{\rarr}{B}\) is expressed as \(n \overset{\rarr}{A}\) and they are antiparallel, it follows that \(n\) must be a negative scalar. Therefore, we can conclude that \(n < 0\).

### Final Answer:
Thus, the value of \(n\) is a negative scalar.