Which of the following statements is a true statement?
A.
A vector can have positive or negative magnitudes.
B.
A vector's magnitude cannot be more than the magnitude of one of its components.
C.
If the x-component of a vector is smaller than its y-component then that vector is in the opposite direction to its y-component.
D.
The magnitude of a vector cannot be zero unless all of its components are zero.
To determine which of the statements is true, let's analyze each option:
A. A vector can have positive or negative magnitudes.
This statement is true. A vector can represent a quantity with both magnitude (size) and direction. The direction can be positive or negative, indicating different orientations or opposite directions.
B. A vector's magnitude cannot be more than the magnitude of one of its components.
This statement is false. The magnitude of a vector can be larger than the magnitude of any of its individual components. The magnitude of a vector is calculated using the Pythagorean theorem, considering both the x-component and y-component of the vector.
C. If the x-component of a vector is smaller than its y-component, then that vector is in the opposite direction to its y-component.
This statement is false. The relationship between the x-component and y-component of a vector does not determine the direction of the vector. The direction of a vector is determined by the sign (+/-) associated with each component or the angle it forms with the x-axis.
D. The magnitude of a vector cannot be zero unless all of its components are zero.
This statement is false. The magnitude of a vector can be zero if and only if all of its components are zero. In other words, the vector has no magnitude or direction in this case.
Therefore, the correct answer is A. A vector can have positive or negative magnitudes.