Chapter 5, Problem 26A

Marshall says that when a pair of vectors are at right angles to each other, the magnitude of their resultant is greater than the magnitude of either vector alone. Renee says he is speaking in generalities and that what he says isn’t always true. With whom do you agree?

To determine

To Choose: The one who is saying correctly.

Explanation of Solution

Introduction:

Let $v_1$ and $v_2$ be two vectors which are right angles to each other.

The resultant of the two can be obtained by their vector addition

  $R=\sqrt{v_1{}^2+v_2{}^2}$

Resultant is the square root of the sum of the square of each vector. Thus, M is right when she says that resultant is always greater than magnitude of individual vector.

Conclusion:

Thus, M is right when she says that resultant is always greater than magnitude of individual vector.