A pair of equal-length vectors at right angles to each other have a resultant. If the angle between the vectors is less than 90°, their resultant is
A)less.
B)the same.
C)greater.

Question

Quizplus · Accepted Answer

Since the vectors are at right angles to each other and have equal length, each vector has a magnitude of 1/sqrt(2) times the magnitude of their resultant (which is the hypotenuse of the right triangle formed by the vectors). Therefore, the magnitudes of the two vectors are 1/sqrt(2) times the magnitude of the resultant.

Now, if the angle between the vectors is less than 90°, the magnitudes of the projections of the vectors onto the resultant are less than their own magnitudes. This means that the two vectors can't cancel each other out completely, so their resultant must be greater than their individual magnitudes (and therefore greater than 1/sqrt(2) times the magnitude of the resultant). Thus, the correct answer is (C) greater.

A Pair of Equal-Length Vectors at Right Angles to Each