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The magnitude of a vector cannot be :...

The magnitude of a vector cannot be :

A

positive

B

unity

C

negative

D

zero

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the magnitude of a vector, we need to analyze the properties of vectors and their magnitudes step by step. ### Step-by-Step Solution: 1. **Understanding Vectors**: - A vector is a quantity that has both magnitude and direction. Examples include displacement, velocity, and force. 2. **Magnitude of a Vector**: - The magnitude of a vector is a measure of its size or length. It is always a non-negative value. 3. **Possible Values for Magnitude**: - **Positive Magnitude**: A vector can have a positive magnitude. For example, a vector with a magnitude of 5 units is valid. - **Unity Magnitude**: A vector can have a magnitude of 1, which is known as a unit vector. For instance, a unit vector in the direction of the x-axis can be represented as \( \hat{i} \) with a magnitude of 1. - **Zero Magnitude**: A vector can have a magnitude of zero, which is referred to as a null vector. This means the vector has no length and does not point in any direction. 4. **Negative Magnitude**: - The magnitude of a vector cannot be negative. Magnitude is a measure of size, and size cannot be negative. Therefore, this option is not valid. 5. **Conclusion**: - Based on the analysis, the only option that is not possible for the magnitude of a vector is negative magnitude. Thus, the correct answer is that the magnitude of a vector cannot be negative. ### Final Answer: The magnitude of a vector cannot be negative.
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