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) A vector’s magnitude cannot be less than the sum of the magnitude of its components. D) 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. E) The magnitude of a vector cannot be zero unless all of its components are zero.If a vector A has components Ax > 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90°. B) 90° to 180°. C) 180° to 270°. D) 270° to 360°. E) cannot be determined without additional information.If a vector A has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90°. B) 90° to 180°. C) 180° to 270°. D) 270° to 360°. E) cannot be determined without additional information.Vector B is obtained by rotating vector A counterclockwise by 270°. The components of B will A) have the same signs as those of A. B) have opposite signs as those of A. C) The x-components will have opposite signs but the y-components will not. D) The y-components will have opposite signs but the x-components will not. E) depend on the quadrant where A is.

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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) A vector’s magnitude cannot be less than the sum of the magnitude of its components.
D) 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.
E) The magnitude of a vector cannot be zero unless all of its components are zero.

If a vector A has components Ax > 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information.

If a vector A has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information

Vector B is obtained by rotating vector A counterclockwise by 270°. The components of B will
A) have the same signs as those of A.
B) have opposite signs as those of A.
C) The x-components will have opposite signs but the y-components will not.
D) The y-components will have opposite signs but the x-components will not.
E) depend on the quadrant where A is.

EXPERT ANSWER


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) A vector’s magnitude cannot be less than the sum of the magnitude of its components.
D) 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.
E) The magnitude of a vector cannot be zero unless all of its components are zero.

Answer :E) The magnitude of a vector cannot be zero unless all of its components are zero.

If a vector A has components Ax > 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information.

Answer :A) 0° to 90°.

If a vector A has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range
A) 0° to 90°.
B) 90° to 180°.
C) 180° to 270°.
D) 270° to 360°.
E) cannot be determined without additional information

Answer :C) 180° to 270°

Vector B is obtained by rotating vector A counterclockwise by 270°. The components of B will
A) have the same signs as those of A.
B) have opposite signs as those of A.
C) The x-components will have opposite signs but the y-components will not.
D) The y-components will have opposite signs but the x-components will not.
E) depend on the quadrant where A is.

Answer : E) depend on the quadrant where A is.