Two vectors A and B are added together giving vector C. The magnitude of C is such that C = sqrt(A2+B2). If the magnitudes of both vectors A and B are doubled, the magnitude of vector C will

A) increase by a factor of 8.

B) increase by a factor of 4.

C) increase by a factor of 2.

D) increase by a factor of sqrt(2).

E) not change.

If three vectors add up to a zero resultant it is correct to say that

A) it is impossible to find three vectors that add up to a zero resultant.

B) the three vectors must be co-linear.

C) the three vectors must be in a plane.

D) the three vectors must have the same magnitude.

E) the three vectors cannot have the same magnitude.

Three vectors have equal magnitudes and make 120° with each other. We can say that

A) the magnitude of the resultant is one-third the magnitude of the component vectors.

B) the magnitude of the resultant is three times the magnitude of the component vectors.

C) the magnitude of the resultant is more than three times the magnitude of each component vector.

D) the resultant is zero.

E) the magnitude of the resultant is equal to the magnitude of the component vectors.

**EXPERT ANSWER **

**Answer :**A) 2

Two vectors A and B are added together giving vector C. The magnitude of C is such that C = sqrt(A2+B2). If the magnitudes of both vectors A and B are doubled, the magnitude of vector C will

A) increase by a factor of 8.

B) increase by a factor of 4.

C) increase by a factor of 2.

D) increase by a factor of sqrt(2).

E) not change.

**Answer :**C) increase by a factor of 2.

If three vectors add up to a zero resultant it is correct to say that

A) it is impossible to find three vectors that add up to a zero resultant.

B) the three vectors must be co-linear.

C) the three vectors must be in a plane.

D) the three vectors must have the same magnitude.

E) the three vectors cannot have the same magnitude.

**Answer :**C) the three vectors must be in a plane.

Three vectors have equal magnitudes and make 120° with each other. We can say that

A) the magnitude of the resultant is one-third the magnitude of the component vectors.

B) the magnitude of the resultant is three times the magnitude of the component vectors.

C) the magnitude of the resultant is more than three times the magnitude of each component vector.

D) the resultant is zero.

E) the magnitude of the resultant is equal to the magnitude of the component vectors.

**Answer : **D) the resultant is zero.