Chapter 3, Problem 1FTD

Under what conditions is the magnitude of the vector sum $\stackrel{\to }{A}$ + $\stackrel{\to }{B}$ equal to the sum of the magnitudes of the two vectors?

To determine

To explain:

The conditions for the magnitude of the vectors sum $\overrightarrow{A}+\overrightarrow{B}$ is same as the sum of magnitudes of vectors $\overrightarrow{A}$ and $\overrightarrow{B}$.

Explanation of Solution

The statement satisfies under the following conditions:

• The two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are collinear which means the vectors should lie on the same plane in the same or opposite direction.
• Simply add the magnitudes of vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ thereby the resultant sum vector also lies on the same plane.

Conclusion:

The condition exists for the vectors passing in same or opposite direction.