Question
What happens to a negative vector that is multiplied by 1?
Only the direction of the vector changes.
The magnitude and direction of the vector change.
No properties of the vector change.
Only the magnitude of the vector changes.
Only the direction of the vector changes.
The magnitude and direction of the vector change.
No properties of the vector change.
Only the magnitude of the vector changes.
Answers
GPT-4o
When a negative vector is multiplied by 1, neither its magnitude nor its direction changes. Therefore, no properties of the vector change.
To illustrate, consider a vector \( \mathbf{v} = -3\mathbf{i} - 4\mathbf{j} \). Multiplying this vector by 1:
\[ 1 \cdot \mathbf{v} = 1 \cdot (-3\mathbf{i} - 4\mathbf{j}) = -3\mathbf{i} - 4\mathbf{j} = \mathbf{v} \]
The vector remains the same.
So the correct answer is:
No properties of the vector change.
To illustrate, consider a vector \( \mathbf{v} = -3\mathbf{i} - 4\mathbf{j} \). Multiplying this vector by 1:
\[ 1 \cdot \mathbf{v} = 1 \cdot (-3\mathbf{i} - 4\mathbf{j}) = -3\mathbf{i} - 4\mathbf{j} = \mathbf{v} \]
The vector remains the same.
So the correct answer is:
No properties of the vector change.