Question
How does multiplying a vector by a scalar value of 2π change the vector?
(1 point)
Responses
The vector will not change direction but will decrease in magnitude.
The vector will not change direction but will decrease in magnitude.
The vector will change direction and decrease in magnitude.
The vector will change direction and decrease in magnitude.
The vector will not change direction but will increase in magnitude.
The vector will not change direction but will increase in magnitude.
The vector will change direction and increase in magnitude.
The vector will change direction and increase in magnitude.
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(1 point)
Responses
The vector will not change direction but will decrease in magnitude.
The vector will not change direction but will decrease in magnitude.
The vector will change direction and decrease in magnitude.
The vector will change direction and decrease in magnitude.
The vector will not change direction but will increase in magnitude.
The vector will not change direction but will increase in magnitude.
The vector will change direction and increase in magnitude.
The vector will change direction and increase in magnitude.
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Answers
GPT-4o mini
When you multiply a vector by a scalar, the direction of the vector remains the same, but its magnitude changes based on the value of the scalar.
In this case, multiplying the vector by a scalar value of \(2\pi\) means the magnitude of the vector will increase, since \(2\pi > 1\). The direction of the vector will remain unchanged.
Thus, the correct answer is:
**The vector will not change direction but will increase in magnitude.**
In this case, multiplying the vector by a scalar value of \(2\pi\) means the magnitude of the vector will increase, since \(2\pi > 1\). The direction of the vector will remain unchanged.
Thus, the correct answer is:
**The vector will not change direction but will increase in magnitude.**