Vectors and have equal magnitudes. Which statement is always true?
A) .
B) .
C) is perpendicular to .
D) is perpendicular to .
E) The magnitude of equals the magnitude of .

Question

Vectors  and  have equal magnitudes. Which statement is always true?
A) . 
B) . 
C) is perpendicular to . 
D) is perpendicular to . 
E) The magnitude of equals the magnitude of .

Quizplus · Accepted Answer

Since the magnitudes of the two vectors are equal, they lie on the same circle centered at the origin. Therefore, the difference between the two vectors must be perpendicular to the line passing through their midpoints, which is a vector connecting the two vectors. This means that the vector 11eb6adc_edac_dbe1_b0cf_8dc2e90ee27f_TB8245_11 (or its negative) is perpendicular to the vector 11eb6adc_edad_02f2_b0cf_21be01a18268_TB8245_11, which is the midpoint vector. This relationship is always true, regardless of the actual values of the vectors.

Vectors and Have Equal Magnitudes