Given vector , the vector
A) has a magnitude 3 times that of .
B) points in the same direction as .
C) has components each of which is 3 times those of .
D) makes the same angle with a given axis as does .
E) is described by all of these.

Question

Given vector  , the vector 
A) has a magnitude 3 times that of . 
B) points in the same direction as . 
C) has components each of which is 3 times those of . 
D) makes the same angle with a given axis as does . 
E) is described by all of these.

Quizplus · Accepted Answer

A) We cannot determine the magnitude of the vectors solely based on their components.
B) Since the second to last component (a812) is larger than that of 11eb1367_5169_a811_8021_7583961a6a7f_TB7291_11 and they have the same sign, the two vectors point in the same direction.
C) Each component of the second vector is obtained by adding 1 to the corresponding component of the first vector and then multiplying by 3. Therefore, each component of the second vector is 3 times that of the first vector.
D) We cannot determine the angle the vectors make with a given axis solely based on their components.
E) All of the above statements are true.

Given Vector , the Vector