Chapter 8.1, Problem 39E

To determine

To state: whether the given information is true always, sometimes or never. Justify the answer with the help of diagram.

Answer to Problem 39E

Sometimes

Explanation of Solution

Given information:

  $\left|\overrightarrow{a}+\overrightarrow{b}\right|=\left|\overrightarrow{a}\right|+\left|\overrightarrow{b}\right|$

Calculation:

The magnitude of the sum of two vectors creates a triangle as shown below. According to the rule, the sum of any two sides of triangle should be greater than the length of third side.

So as long as length of both the vectors is greater than zero, then $\left|\overrightarrow{a}+\overrightarrow{b}\right|\ne \left|\overrightarrow{a}\right|+\left|\overrightarrow{b}\right|$ occurs.

If $\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|=0$ , then $\left|\overrightarrow{a}+\overrightarrow{b}\right|=\left|\overrightarrow{a}\right|+\left|\overrightarrow{b}\right|$ .