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.

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.

**Answer :**A) 0° to 90°.

**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.